We investigate the thermodynamic properties of 3+1 dimensional black holes in asymptotically de Sitter spacetimes, conformally coupled to a real scalar field. We use a Euclidean action approach, where boundary value data is specified at a finite radius `cavity' outside the black hole, working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. For the MTZ subclass of solutions, we find Hawking-Page-like phase transitions from a black hole spacetime to thermal de Sitter with a scalar field. In the more general case, Hawking-Page-like phase transitions are also present, whose existence depends further on a particular cosmic censorship bound.
We use a simplified formalism to re-compute the single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on de Sitter background which was originally made by Boran, Kahya and Park [1-3]. Our result resolves the problem with the flat space correspondence limit that was pointed out by Fröb [4]. We discuss how this computation will be used in a long-term project to purge the linearized effective field equation of gauge dependence.
We study the thermodynamics of de Sitter black holes with a conformally coupled scalar field. The geometry is that of the ``lukewarm'' Reissner-Nordstrom-de Sitter black holes, with the event and cosmological horizons at the same temperature. This means that the region between the event and cosmological horizons can form a regular Euclidean instanton. The entropy is modified by the non-minimal coupling of the scalar field to the geometry, but can still be derived from the Euclidean action, provided suitable modifications are made to deal with the electrically charged case. We use the first law…
The present work is the second part of a series of computations for the self-mass-squared of the conformally coupled (CC) scalar interacting with gravitons. This work includes the kinetic-kinetic and kinetic-conformal parts, and thus completes the full scalar self-mass squared at one loop order in de Sitter background when combined with the conformal-conformal part previously evaluated. We use dimensional regularization and renormalize the results by subtracting appropriate counterterms. The self-mass squared is finally ready to quantum-correct the CC scalar field equation so that one can stud…
A four-dimensional black hole solution of the Einstein equations with a positive cosmological constant, coupled to a conformal scalar field, is given. There is a curvature singularity at the origin, and scalar field diverges inside the event horizon. The electrically charged solution, which has a fixed charge-to-mass ratio is also found. The quartic self-interacting coupling becomes bounded in terms of Newton's and the cosmological constants.
We evaluate one loop quantum gravity corrections to the conformally coupled (CC) scalar self-mass-squared on a locally de Sitter background. In this paper we consider only the conformal-conformal interaction part of the self-mass-squared. This complements the minimal-minimal part worked out in the previous paper [E. O. Kahya and R. P. Woodard, Phys. Rev. D 76, 124005 (2007), arXiv: 0709.0536], and we will add the minimal-conformal part in a follow-up paper to complete the full self-mass-squared at one loop order. The computation is performed using dimensional regularization and the results are…
In this article, we quantize the Maxwell ("massless spin one") de Sitter field in a conformally invariant gauge. This quantization is invariant under the SO$_0(2,4)$ group and consequently under the de Sitter group. We obtain a new de Sitter invariant two-points function which is very simple. Our method relies on the one hand on a geometrical point of view which uses the realization of Minkowski, de Sitter and anti-de Sitter spaces as intersections of the null cone in $\setR^6$ and a moving plane, and on the other hand on a canonical quantization scheme of the Gupta-Bleuler type.
We study conformally-coupled massive scalar field theory with the mass term treated as a perturbation in the expanding half of de Sitter spacetime as a toy model for comparing various perturbative formalisms. We point out that the in-out perturbation theory breaks down due to infrared divergences coming from the infinite future. We then clarify the relation between the free-theory vacuum and the true vacuum using the Bogolubov transformation and show that the discrepancy between the free-theory out-vacuum and the true vacuum causes apparent pair creation of free-theory particles and makes the …
The Einstein-conformally coupled scalar field system is studied in the presence of a cosmological constant. We consider a massless or massive scalar field with no additional self-interaction, and spherically symmetric black hole geometries. When the cosmological constant is positive, no scalar hair can exist and the only solution is the Schwarzschild-de Sitter black hole. When the cosmological constant is negative, stable scalar field hair exists provided the mass of the scalar field is not too large.
We provide a classification of $Λ>0$-vacuum spacetimes which admit a Killing vector field with respect to which the associated "Mars-Simon tensor" (MST) vanishes and having a conformally flat $\mathcal{J}^-$ (or $\mathcal{J}^+$). To that end, we also give a complete classification of conformal Killing vector fields on the $3$-sphere $\mathbb{S}^3$ up to Möbius transformations shedding light on the two fundamental constants that characterize the family of Kerr-de Sitter-like spacetimes, which turn out to be well-defined geometrical invariants. The topology of $\mathcal{J}$ is determined in ever…
We construct a four dimensional de Sitter space upto a conformal transformation by compactifying the anisotropic SD3-brane solution of type IIB string theory on a six dimensional product space of the form $H_5 \times S^1$, where $H_5$ is a five dimensional hyperbolic space and $S^1$ is a circle. The radius of the hyperbolic space is chosen to be constant. The radius of the circle and the dilaton in four dimensions are time dependent and not constant in general. By different choices of parameters characterizing the SD3-brane solution either the dilaton or the radius of the circle can be made co…
Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been calculated. The ``Hilbert'' space structure and the field operator, in terms of coordinate independent de Sitter plane waves, have been defined. The construction of the paper is based on the analyticity in the complexified pseudo-Riemanian manifold, presented first by Bros et al.. Minkowskian limits of these functions are analyzed. The relation between the ambie…
Utilizing the conformal-flatness nature of 3-dim. Anti-de Sitter (AdS_3) black hole solution of Banados, Teitelboim and Zanelli, the quantisation of conformally-coupled scalar and spinor fields in this background spacetime is explicitly carried out. In particular, mode expansion forms and propagators of the fields are obtained in closed forms. The vacuum in this conformally-coupled field theories in AdS_3 black hole spacetime, which is conformally-flat, is the conformal vacuum which is unique and has global meaning. This point particularly suggests that now the particle production by AdS_3 bla…
''Massless'' spin-2 field equation in de Sitter space, which is invariant under the conformal transformation, has been obtained. The frame work utilized is the symmetric rank-2 tensor field of the conformal group. Our method is based on the group theoretical approach and six-cone formalism, initially introduced by Dirac. Dirac's six-cone is used to obtain conformally invariant equations on de Sitter space. The solution of the physical sector of massless spin-2 field (linear gravity) in de Sitter ambient space is written as a product of a generalized polarization tensor and a massless minimally…
We compute exact expressions of the noise kernel, defined as the expectation value of the symmetrized connected stress energy bitensor, for conformally-invariant scalar fields with respect to the conformal vacuum, valid for an arbitrary separation (timelike, spacelike and null) of points in a class of conformally-flat spacetimes. We derive explicit expressions for the noise kernel evaluated in the static de Sitter coordinates with respect to the Gibbons-Hawking vacuum and analyze the behavior of the noise kernel in the region near the cosmological horizon. We develop a quasi-local expansion ne…
Using asymptotic characterization results of spacetimes at conformal infinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-one correspondence with spacetimes in the Kerr-de Sitter-like class with conformally flat $\mathscr{I}$. Kerr-Schild-de Sitter are spacetimes of Kerr-Schild form with de Sitter background that solve the $(Λ>0)$-vacuum Einstein equations and admit a smooth conformal compactification sharing $\mathscr{I}$ with the background metric. Kerr-de Sitter-like metrics with conformally flat $\mathscr{I}$ are a generalization of the Kerr-de Sitter metrics, defined ori…
We show that for non-conformally flat bulk spacetime, there exist no bound modes for zero mass graviton on the 3-brane. The brane world model is therefore unstable for the bulk spacetime being different from the conformally flat anti - de Sitter space.
We study the stability of new neutral and electrically charged four-dimensional black hole solutions of Einstein's equations with a positive cosmological constant and conformally coupled scalar field. The neutral black holes are always unstable. The charged black holes are also shown analytically to be unstable for the vast majority of the parameter space of solutions, and we argue using numerical techniques that the configurations corresponding to the remainder of the parameter space are also unstable.
A framework conceptually based on the conformal techniques employed to study the structure of the gravitational field at infinity is set up in the context of loop quantum gravity to describe asymptotically anti-de Sitter quantum spacetimes. A conformal compactification of the spatial slice is performed, which, in terms of the rescaled metric, has now finite volume, and can thus be conveniently described by spin networks states. The conformal factor used is a physical scalar field, which has the necessary asymptotics for many asymptotically AdS black hole solutions.
In this paper we write down the equation for a scalar conformally coupled field simultaneously for de Sitter (dS), anti-de Sitter (AdS) and Minkowski spacetime in d-dimensions. The curvature dependence appears in a very simple way through a conformal factor. As a consequence the process of curvature free limit, including wave functions limit and two-points functions, turns to be a straightforward issue. We determine a set of modes, that we call de Sitter plane waves, which become ordinary plane waves when the curvature vanishes.
We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model conformally coupled to Weyl gravity. We show that the equations of motion admit solutions spontaneously breaking the conformal symmetry and the gauge symmetry, providing a mechanism for supplying a scale in the theory. The vacuum solution corresponds to anti-de-Sitter space-time, while localized soliton solutions correspond to magnetic monopoles in asymptoticall…
The vacuum energy for a massless conformally coupled scalar field in a brane world set up, corresponding to de Sitter branes in a bulk anti-de Sitter spacetime, is calculated. We use the Euclidean version of the metric which can be conformally related to a metric similar in form to the Einstein universe (S^4 times R). Employing zeta-function regularisation we evaluate the one-loop effective potential and show that the vacuum energy is zero for the one brane and non-zero for the two brane configuration. We comment on the back-reaction of this Casimir energy and on the inclusion of a mass term o…
In this paper we have studied a black hole in de Sitter space which has a conformally coupled scalar field in the background. This black hole is also known as the $MTZ$ black hole. We have obtained exact values for the quasi normal mode frequencies under massless scalar field perturbations. We have demonstrated that when the black hole is near-extremal, that the wave equation for the massless scalar field simplifies to a Schr$\ddot{o}$dinger type equation with the well known P$\ddot{o}$shler-Teller potential. We have also used 6th order WKB approximation to compute quasinormal mode frequencies…
We study the thermodynamics and dynamics of high-dimensional Einstein-power-Yang-Mills black holes in conformal gravity. Specifically, we investigate a class of conformally related black holes whose metrics differ by a scale factor. We show that a suitable scale factor cures the geodesic incompleteness and the divergence of Kretschmann scalars at the center of black holes. In the aspect of thermodynamics, we analyse the Hawking temperature, the entropy, and the specific heat, and verify the existence of second-order phase transitions. We find that the thermodynamics of this class of conformall…
We study the corrected entropy due to thermal fluctuation and their effect on the thermodynamics of a conformally dressed black hole in three dimensions. We find that the thermal fluctuation affects the entropy significantly for small black holes. Various corrected thermodynamical variables are also calculated for this black hole. We observe that thermal fluctuation on the thermodynamics of a small conformal black hole has a significant effect. We also analyse the stability of black hole under the effect of thermal fluctuation. Due to thermal fluctuation, instability occurs in the system of sm…
Based on some recent work of the authors, we focus on the relationship between the Casimir energy of a Majorana spinor field for a Euclidean Einstein universe $S^4\times R$ and for a Euclidean de Sitter brane ($S^4$) embedded in AdS(5). This is for a conformally coupled massless field. Interestingly, the one brane effective potential is zero and the results are equivalent, as for the scalar case, when evaluated on the conformally related cylinder. However, using the actual metric this equivalence no longer holds because a non-trivial contribution from the path integral measure (known as the co…
We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat $n$-metric $γ$ of signature $(r,s)$ modulo conformal transformations of $γ$. This is done in terms of endomorphisms in the pseudo-orthogonal Lie algebra $\mathfrak{o}(r+1,s+1)$ up to conjugation of the its group $O(r+1,s+1)$. The explicit classification is worked out in full for the Riemannian $γ$ case ($r = 0, s = n$). As an application of this result, we prove that the set of five dimensional, $(Λ>0)$-vacuum, algebraically special metrics with non-degenerate optical …
We present a new family of exact four-dimensional Taub-NUT spacetimes in Einstein-$Λ$ theory supplemented with a conformally coupled scalar field exhibiting a power-counting super-renormalizable potential. The construction proceeds as follows: A solution of a conformally coupled theory with a conformal potential, henceforth the seed $(g_{μν},ϕ)$, is transformed by the action of a specific change of frame in addition with a simultaneous shift of the seed scalar. The new configuration, $(\bar{g}_{μν},\barϕ)$, solves the field equations of a conformally coupled theory with the aforementioned supe…
We have considered the quantum behavior of a conformally induced gravity in the minimal Riemann-Cartan space. The regularized one-loop effective potential considering the quantum fluctuations of the dilaton and the torsion fields in the Coleman-Weinberg sector gives a sensible phase transition for an inflationary phase in De Sitter space. For this effective potential, we have analyzed the semi-classical equation of motion of the dilaton field in the slow-rolling regime.
We extend the derivation of the Hawking temperature of a Schwarzschild black hole via the Heisenberg uncertainty principle to the de Sitter and anti-de Sitter spacetimes. The thermodynamics of the Schwarzschild-(anti-)de Sitter black holes is obtained from the generalized uncertainty principle of string theory and non-commutative geometry. This may explain why the thermodynamics of (anti-)de Sitter-like black holes admits a holographic description in terms of a dual quantum conformal field theory, whereas the thermodynamics of Schwarzschild-like black holes does not.
We work on the relation between the local thermodynamic instability and the dynamical instability of large black holes in four-dimensional anti-de Sitter space proposed by Gubser and Mitra. We find that all perturbations suppressing the metric fluctuations at linear order become dynamically unstable when black holes lose the local thermodynamic stability. We discuss how dynamical instabilities can be explained by the Second Law of Thermodynamics.
Conformally invariant GUT-like model including gravity based on Riemann - Cartan space-time $U_4$ is considered. Cosmological scenario that follows from the model is discussed and standard quantum gravitational formalism in the Arnowitt-Deser-Misner form is developed. General formalism is then illustrated on Bianchi-IX minisuperspace cosmological model. Wave functions of the universe in the de Sitter minisuperspace model with Vilenkin and Hartle-Hawking boundary conditions are considered and corresponding probability distributions for the scalar field values are calculated.
We discuss the existence, stability and classical thermodynamics of four-dimensional, spherically symmetric black hole solutions of the Einstein equations with a conformally coupled scalar field. We review the solutions existing in the literature with zero, positive and negative cosmological constant. We also outline new results on the thermodynamics of these black holes when the cosmological constant is non-zero.
We consider four dimensional stationary and axially symmetric spacetimes for conformally coupled scalar-tensor theories. We show that, in analogy to the Lewis-Papapetrou problem in General Relativity (GR), the theory at hand can be recast in an analogous integrable form. We give the relevant rod formalism, introduced by Weyl for vacuum GR, explicitly giving the rod structure of the black hole of Bocharova et al. and Bekenstein (BBMB), in complete analogy to the Schwarzschild solution. The additional scalar field is shown to play the role of an extra Weyl potential. We then employ the Ernst met…
In this paper, we present a class of rotating solutions in Gauss--Bonnet gravity in the presence of cosmological constant and conformally invariant Maxwell field and study the effects of the nonlinearity of the Maxwell source on the properties of the spacetimes. These solutions may be interpret as black brane solutions with inner and outer event horizons provide that the mass parameter $m$ is greater than an extremal value $m_{ext}$, an extreme black brane if $m=m_{ext}$ and a naked singularity otherwise. We investigate the conserved and thermodynamics quantities for asymptotically flat and as…
We present arguments for the existence of both globally regular and black hole solutions of the Einstein equations with a conformally coupled scalar field, in the presence of a negative cosmological constant, for space-time dimensions greater than or equal to four. These configurations approach asymptotically anti-de Sitter spacetime and are indexed by the central value of the scalar field. We also study the stability of these solutions, and show that, at least for all the solutions studied numerically, they are linearly stable.
Brief comments on a plausible holographic relationship between the opposite rotational dragging effect of a (2+1)-dimensional rotating de Sitter space and the non-unitarity of a boundary conformal field theory are given. In addition to the comments, we study how the opposite rotational dragging effect affects the statistical-mechanical quantities in the rotating de Sitter space in comparison with a BTZ black hole.
We show in this note that the Padmanabhan expression $E = a/2$ for the energy of the Schwarzschild and de Sitter spacetimes (a - the horizon radius) is also valid for the Rindler horizon, using an analogy with the electrostatic case.
In this paper we propose a straightforward method for understanding the thermodynamics of black holes in de Sitter space, one that will allow us to study these black holes in a way that is analogous to the anti-de Sitter case. As per usual, we formulate separate thermodynamic first laws for each horizon present in the spacetime, and study their thermodynamics as if they were independent systems characterized by their own temperature. That these systems are not entirely independent and various thermodynamic quantities in them are in fact "correlated" is reflected by the fact that their thermody…
In the de Sitter ambient space formalism the massless fields, which include the linear gravity and massless minimally coupled scalar field, can be written in terms of two separate parts: a massless conformally coupled scalar field and a polarization tensor(-spinor) part. Therefore due to the massless conformally coupled scalar field, there exist an unique Bunch-Davies vacuum state for quantum field theory in the de Sitter space time. In the de Sitter ambient space formalism one can show that the massless fields with spin $s\geq 1$ are gauge invariant. By coupling the massless gauge spin-$2$ an…
We investigate the thermodynamics of spherically symmetric black hole solutions in a four-dimensional Einstein--Yang-Mills-SU(2) theory with a negative cosmological constant. Special attention is paid to configurations with a unit magnetic charge. We find that a set of Reissner-Nordström--Anti-de Sitter black holes can become unstable to forming non-Abelian hair. However, the hairy black holes are never thermodynamically favoured over the full set of abelian monopole solutions. The thermodynamics of the generic configurations possessing a noninteger magnetic charge is also discussed.
We investigate the first law of thermodynamics in the case of the (2+1)-dimensional BTZ black holes and Kerr-de Sitter spacetimes, in particular, we focus on the integral mass formulas. It is found that by assuming the cosmological constant as a variable state parameter, both the differential and integral mass formulas of the first law of black hole thermodynamics in the asymptotic flat spacetimes can be directly extended to those of rotating black holes in anti-de Sitter and de Sitter backgrounds. It should be pointed that these formulas come into existence in any dimensions also.
Conditions for thermodynamic stability of asymptotically anti-de Sitter rotating black holes in D-dimensions are determined. Local thermodynamic stability requires not only positivity conditions on the specific heat and the moment of inertia tensor but it is also necessary that the adiabatic compressibility be positive. It is shown that, in the absence of a cosmological constant, neither rotation nor charge is sufficient to ensure full local thermodynamic stability of a black hole. Thermodynamic stability properties of anti-de Sitter Myers-Perry black holes are investigated for both singly spi…
A curved static de Sitter-like metric is analyzed. The source of curvature is rooted from a constant stress tensor with positive energy density and negative pressures. All the curvature invariants are constant everywhere and the geometry is conformally flat. The horizon surface gravity equals the parameter $ω$ from the metric that is also interpreted as an angular velocity. The Tolman-Komar gravitational energy is investigated. One finds that the horizon entropy satisfies the relation $S = A_{H}/4$, as for the black hole horizon.
Thermodynamic geometry is applied to the Born-Infeld-anti-de Sitter black hole (BIAdS) in the four dimensions, which is a nonlinear generalization of the Reissner-NorstrÄom-AdS black hole (RNAdS). We compute the Weinhold as well as the Ruppeiner scalar curvature and find that the singular points are not the same with the ones obtained using the heat capacity. Legendre-invariant metric proposed by Quevedo and the metric obtained by using the free energy as the thermodynamic potential are obtained and the corresponding scalar curvatures diverge at the Davies points.
Dirac's theory of constrained Hamiltonian systems is applied to the minimal conformally invariant SU(5) grand-unified model studied at 1-loop level in a de Sitter universe. For this model, which represents a simple and interesting example of GUT theory and at the same time is a step towards theories with larger gauge group like SO(10), second-class constraints in the Euclidean-time regime exist. In particular, they enable one to prove that, to be consistent with the experimentally established electroweak standard model and with inflationary cosmology, the residual gauge-symmetry group of the e…
We investigate the thermodynamics of the Einstein-non linear-Maxwell-Yukawa black hole solution in de-Sitter spacetime. After presenting the black hole solution and its horizons, we use different thermodynamics points of view to probe the phase structure of such a black hole, ranging from local, global thermodynamics to the effective thermodynamics formalism with two horizons. Our analysis shows that the black hole can undergo a thermal phase transition between an unstable phase and stable phase. These results are consolidated by our proposal of generalizing effective thermodynamics to three h…
As in the grand canonical treatment of Reissner - Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.
In this paper, we investigate the thermodynamical properties of Schwarzschild-Beltrami-de Sitter black hole introduced by Mu-Lin Yan \textit{et al.} in 2013 by introducing inertial Beltrami coordinates to traditional non-inertial Schwarzschild-de Sitter metric which is the exact static spherical symmetry solution of Einstein equation with a positive cosmological constant $Λ$. Based on this new metric, we compute entropy on all horizons and we give the entropy bound of the black hole. Hawking temperatures are calculated by considering a perturbation to entropy relations due to that the spacetim…
When Lorentz invariance is violated at high energy, the laws of black hole thermodynamics are apparently no longer satisfied. To shed light on this observation, we study dispersive fields in de Sitter space. We show that the Bunch-Davies vacuum state restricted to the static patch is no longer thermal, and that the Tolman law is violated. However we also show that, for free fields at least, this vacuum is the only stationary stable state, as if it were in equilibrium. We then present a precise correspondence between dispersive effects found in de Sitter and in black hole metrics. This indicate…
In this paper time machines are constructed from anti-de Sitter space. One is constructed by identifying points related via boost transformations in the covering space of anti-de Sitter space and it is shown that this Misner-like anti-de Sitter space is just the Lorentzian section of the complex space constructed by Li, Xu, and Liu in 1993. The others are constructed by gluing an anti-de Sitter space to a de Sitter space, which could describe an anti-de Sitter phase bubble living in a de Sitter phase universe. Self-consistent vacua for a massless conformally coupled scalar field are found for …
Completely from the thermodynamic point of view, we explore the microscopic character of a hairy black hole of Einstein's theory conformally coupled to a scalar field in five dimensions by means of the Ruppeiner thermodynamic geometry. We demonstrate that the scalar hairy black hole has rich microscopic structures in different parameter spaces. Moreover, we analyze the thermal stability of this black hole in detail.
In this work, we provide new examples of Anti-de Sitter black holes with a planar base manifold in four-dimensional Critical Gravity by considering nonlinear electrodynamics as a matter source. We find a general solution characterized by the presence of only one integration constant where, for a suitable election of coupling constants, we can show the existence of one or more horizons. Additionally, we compute its non-null thermodynamical quantities through a variety of techniques, testing the validity of the first law of thermodynamics as well as a Smarr formula. Finally, we analyze the local…
We investigate the thermodynamics and stability of the horizons in warped anti-de Sitter black holes of the new massive gravity under the scattering of a massive scalar field. Under scattering, conserved quantities can be transferred from the scalar field to the black hole, which change the state of the black hole. We determine that the changes in the black hole are well coincident with the laws of thermodynamics. In particular, the Hawking temperature of the black hole cannot be zero in the process as per the third law of thermodynamics. Furthermore, the black hole cannot be overspun beyond t…
Scattering data can be generically described in terms of monodromies. Here we obtain scattering amplitudes for conformally coupled scalar fields in Kerr-de Sitter black holes using this monodromy technique. The only non-trivial parameter, the composite monodromy parameter $σ_{ij}$ between two regular singular points, can be solved implicitily in terms of the Painlevé VI $τ$-function. The application of the Virasoro conformal blocks to solve the latter can now be interpreted as a verification of the striking relationship between conformal symmetry and black holes.
By using a new approach, we demonstrate analytic expressions for slowly rotating Gauss-Bonnet charged black holes with negative cosmological constant. Up to the linear order of the rotating parameter a, the mass, Hawking temperature and entropy of the charged black holes get no corrections from rotation.
We study conformal gravity as an alternative theory of gravitation. For conformal gravity to be phenomenologically viable requires that the conformal symmetry is not manifest at the energy scales of the other known physical forces. Hence we require a mechanism for the spontaneous breaking of conformal invariance. In this paper we study the possibility that conformal invariance is spontaneously broken due to interactions with conformally coupled matter fields. The vacuum of the theory admits conformally non-invariant solutions corresponding to maximally symmetric space-times and variants thereo…
The Schwarzschild-de Sitter (SdS) black hole solution, which has two event horizons, is considered to examine the relation between the quasi-localized energy complexes on ${\cal M}$ and the heat flows passing through its boundary $\partial {\cal M}$. Here ${\cal M}$ is the patch between cosmological event horizon and black hole event horizon of the SdS black hole solution. Conclusively, the relation, like the Legendre transformation, between the quasi-localized Einstein and Møller energy complex and the heat flows passing through the boundary is obeyed, and these two quasi-localized energy com…
