4 pages; v2: Version to appear in Foundations of Physics. Potential counterexamples addressed, argument given applying to LV theories where all speeds (or horizons) coincide, and editing for clarity
Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a microscopic second law of causal horizon thermodynamics.
Lorentz-Violating (Regular) Black Holes in Einstein Gravity
Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）
It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.
In this paper we study the relationship between the Einstein field equations for the (2+1)-dimensional evolving wormhole and the first law of thermodynamics. It has been shown that the Einstein field equations can be rewritten as a similar form of the first law of thermodynamics at the dynamical trapping horizon (as proposed by Hayward) for the dynamical spacetime which describes intrinsic thermal properties associated with the trapping horizon. For a particular choice of the shape and potential functions we are able to express field equations as a similar form of first law of thermodynamics $…
A Lorentz-noninvariant modification of quantum electrodynamics (QED) is considered, which has photons described by the nonbirefringent sector of modified Maxwell theory and electrons described by the standard Dirac theory. These photons and electrons are taken to propagate and interact in a Schwarzschild spacetime background. For appropriate Lorentz-violating parameters, the photons have an effective horizon lying outside the Schwarzschild horizon. A particular type of Compton scattering event, taking place between these two horizons (in the photonic ergoregion) and ultimately decreasing the m…
We investigate the possibility of the acoustic superresonance phenomenon (analog to the superradiance in black hole physics), i.e., the amplification of a sound wave by reflection from the ergoregion of a rotating acoustic black hole with Lorentz symmetry breaking. For rotating black holes the effect of superradiance corresponds to the situation where the incident waves has reflection coefficient greater than one, and energy is extracted from them. For an acoustic Kerr-like black hole its rate of loss of mass is affected by the Lorentz symmetry breaking. We also have shown that for suitable va…
Since Stephen Hawking discovered that black holes emit thermal radiation, black holes have become the theoretical laboratories for testing our ideas on quantum gravity. This dissertation is devoted to the study of singularities, the formation of black holes by gravitational collapse and the global structure of spacetime. All our investigations are in the context of a recently proposed approach to quantum gravity, which breaks Lorentz and diffeomorphism symmetries at very high energies.
BTZ black holes provide excellent frameworks for studying theories that are at the interface of classical and quantum gravity. In this paper we couple the Riemannian spacetime with the bumblebee field, in the background of massive gravity, which produces the violation of spontaneous Lorentz symmetry. In this setup we construct a large family of static vacuum BTZ black hole solutions. We study the asymptotic behaviour of curvature invariants and show that our resulting solutions describe asymptotically AdS (2+1)-dimensional BTZ black holes with negative cosmological constant. For positive cosmo…
We have investigated quantum entropy of a static black hole arising from the massless scalar field with Lorentz violation induced by the coupling to Einstein tensor. Our results show that the coupled massless scalar field contributes to the classical Bekenstein-Hawking term in the black hole entropy. The corrected classical Bekenstein-Hawking entropy is not one quarter of the event horizon area of the original background black hole, but of a corresponding effective metric related to the coupling. It means that the classical Bekenstein-Hawking entropy depends not only on the black hole paramete…
We studied the correction of the quantum tunneling radiation of fermions with spin $1/2$ in Kerr Anti-de-Sitter black hole. First, the dynamic equation of spin $1/2$ fermions was corrected using Lorentz's violation theory. Second, the new expressions of the fermions quantum tunneling rate, the Hawking temperature of the black hole and the entropy of the black hole were obtained according to the corrected fermions dynamic equation. At last, some comments are made on the results of our work.
In Vaidya-Bonner de Sitter Black hole space-time, the tunneling radiation characteristics of fermions and bosons are corrected by taking Lorentz symmetry breaking theory into account. The corresponding gamma matrices and ether-like field vectors of the black hole are constructed, then the new modified form of Dirac equation for the fermion with spin 1/2 and the new modified form of Klein-Gordon equation for boson in the curved space-time of the black hole are obtained. Through solving the two equations, new and corrected expressions of surface gravity, Hawking temperature and tunneling rate of…
Lorentz-violating modifications to particle dynamics, thermodynamics and vacuum energy in bumblebee gravity
Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Khazar University（哈扎尔大学）；Eastern Mediterranean University（东地中海大学）；University of Hradec Králové（赫拉德茨-克拉洛韦大学）；Al-Farabi Kazakh National University（阿里-法拉比哈萨克国立大学）
We consider nonstandard photons from nonbirefringent modified Maxwell theory and discuss their propagation in a fixed Schwarzschild spacetime background. This particular modification of Maxwell theory is Lorentz-violating and allows for maximal photon velocities differing from the causal speed c of the asymptotic background spacetime. In the limit of geometrical optics, light rays from modified Maxwell theory are found to propagate along null geodesics in an effective metric. We observe that not every Lorentz-violating theory with multiple maximal velocities different from the causal speed c m…
The standard argument for the Lorentz invariance of the thermodynamic entropy in equilibrium is based on the assumption that it is possible to perform an adiabatic transformation whose only outcome is to accelerate a macroscopic body, keeping its rest mass unchanged. The validity of this assumption constitutes the very foundation of relativistic thermodynamics and needs to be tested in greater detail. We show that, indeed, such a transformation is always possible, at least in principle. The only two assumptions invoked in the proof are that there is at least one inertial reference frame in whi…
We show that a static spherically symmetric black hole, in a generic theory of gravity with generic matter fields, has a two-dimensional Lorentz symmetry.
The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light) and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in classical and quantum case.
Black holes in Lorentz-violating theories have been claimed to violate the second law of thermodynamics by perpetual motion energy extraction. We revisit this question for a Penrose splitting process in a spherically symmetric setting with two species of particles that move on radial geodesics that extend to infinity. We show that energy extraction by this process cannot happen in any theory in which gravity is attractive, in the sense of a geometric inequality that we describe. This inequality is satisfied by all known Einstein-æther and Hořava black hole solutions.
In this paper, we have applied the Lorentz-invariance-violation (LIV) class of dispersion relations (DR) with the dimensionless parameter n = 2 and the "sign of LIV" η_+ = 1, to phenomenologically study the effect of quantum gravity in the strong gravitational field. Specifically, we have studied the effect of the LIV-DR induced quantum gravity on the Schwarzschild black hole thermodynamics. The result shows that the effect of the LIV-DR induced quantum gravity speeds up the black hole evaporation, and its corresponding black hole entropy undergoes a leading logarithmic correction to the "redu…
We reconsider the possibility of violating the generalized second law of thermodynamics in theories with spontaneous Lorentz violation. It has been proposed that this may be accomplished in particular with a black hole immersed in a ghost condensate background, which may be taken to break Lorentz invariance without appreciably distorting the space-time geometry. In this paper we show that there in fact exist solutions explicitly describing flow of negative energy into these black holes, allowing for violation of the second law in a very simple way. This second law violation is independent of a…
In this paper we derive acoustic black hole metrics in the (3+1) and (2+1)-dimensional Abelian Higgs model with Lorentz symmetry breaking. In this set up the sound waves lose the Lorentz boost invariance and suffer a 'birefringence' effect. We have found acoustic black holes and respective Hawking temperatures depending on the Lorentz violating parameter. Furthermore, we obtain an acoustic Kerr-like black hole metric with the Lorentz violating term affecting its rate of loss of mass. We also have shown that for suitable values of the Lorentz violating parameter a wider spectrum of particle wav…
We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvature 2-form, including general relativity, Lovelock gravity, and "topological" terms in four dimensions.
Motivated by recent activities in Lorentzian Taub-NUT space thermodynamics, we calculate conserved charges of these spacetimes. We find additional mass, nut, angular momentum, electric and magnetic charge densities distributed along Misner string. These additional charges are needed to account for the difference between the values of the above charges at horizon and at infinity. We propose an unconstrained thermodynamical treatment for Taub-NUT spaces, where we introduce the nut charge $n$ as a relevant thermodynamic quantity with its chemical potential ϕ_n. The internal energy in this treatme…
A Kerr-Sen-like black hole solution results from Einstein-bumblebee gravity. It contains a Lorentz violating (LV) parameter that enters when the bumblebee field receives vacuum expectation value through a spontaneously breaking of the symmetry of the classical action. The geometrical structure concerning the singularity of this spacetime is studied with reference to the parameters involved in the Kerr-Sen-like metric. We introduce this Einstein-bumblebee modified gravity to probe the role of spontaneous Lorentz violation on the superradiance scattering phenomena and the instability associated …
When Bumblebee Meets NLED: Lorentz-Violating Black Holes and Regular Spacetimes
Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）
In this paper we explore the effect of the generalized uncertainty principle and modified dispersion relation to compute Hawking radiation from a rotating acoustic black hole in the tunneling formalism by using the Wentzel-Kramers-Brillouin (WKB) approximation applied to the Hamilton-Jacobi method. The starting point is to consider the planar acoustic black hole metric found in a Lorentz-violating Abelian Higgs model. In our analyzes we investigate quantum corrections for the Hawking temperature and entropy. A logarithmic correction and an extra term that depends on a conserved charge were obt…
In this review we summarize, expand, and set in context recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. We specifically consider the thermodynamics of higher-dimensional rotating asymptotically flat and AdS black holes and black rings in a canonical (fixed angular momentum) ensemble. We plot the associated thermodynamic potential-the Gibbs free energy-and study its behaviour to uncover possible thermodynamic phase transitions in th…
In this paper, the tunneling of scalar particles near the event horizons of Riemann space time, BTZ black hole and Schwarzschild-de Sitter black hole are investigated by applying Hamilton-Jacobi equation with Lorentz violation theory in curved space time. The modified Hamilton-Jacobi equation is derived from Klein-Gordon equation of scalar particles induced by Lorentz violation theory in curved space time. The Hawking temperatures of Riemann space time and the BTZ black hole are modified due to the effect of Lorentz violation theory. Moreover, the Bekenstein-Hawking entropy near the event hori…
When the cosmological constant, $Λ$, is interpreted as a thermodynamic variable in the study of black hole thermodynamics a very rich structure emerges. It is natural to interpret $Λ$ as a pressure and define the thermodynamically conjugate variable to be the thermodynamic volume of the black hole (which need not bear any relation to the geometric volume). Recent progress in this new direction for black hole thermodynamics is reviewed.
I give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to (i) the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; (ii) the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; (iii) the central role of Hawking radiation in permitting black holes to be in thermal contact …
We obtain an exact Kerr-like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking. In order to study the effects of this breaking, we consider the black hole shadow and find that the radial of the unstable spherical orbit on the equatorial plane $r_c$ decreases with the Lorentz breaking constant $\ell>0$, and increases with $\ell<0$. These shifts are similar to …
In this work, we extend the analysis of Brown and York to find the quasilocal energy in a spherical box in the Schwarzschild spacetime. Quasilocal energy is the value of the Hamiltonian that generates unit magnitude proper-time translations on the box orthogonal to the spatial hypersurfaces foliating the Schwarzschild spacetime. We call this Hamiltonian the Brown-York Hamiltonian. We find different classes of foliations that correspond to time-evolution by the Brown-York Hamiltonian. We show that although the Brown-York expression for the quasilocal energy is correct, one needs to supplement t…
In this work we study thermodynamics of 2+1-dimensional static black holes with a nonlinear electric field. Besides employing the standard thermodynamic approach, we investigate the black hole thermodynamics by studying its thermodynamic geometry. We compute the Weinhold and Ruppeiner metrics and compare the thermodynamic geometry with the standard description on the black hole thermodynamics. We further consider the cosmological constant as an additional extensive thermodynamic variable. In the thermodynamic equilibrium three dimensional space, we compute the efficiency of the heat engine and…
In this work we research on the thermodynamical properties of the Bardeen black holes. We compute the series of new thermodynamic quantities such as local temperature, heat capacity, off-shell free energy of this kind of black hole in detail. We further analyze the thermodynamical characteristics of the Bardeen black hole by varying its charge $q$ to check the existence and stability of the black hole.
The thermodynamics and phase transitions of charged RN-AdS and rotating Kerr-AdS black holes in a generalized Randall-Sundrum braneworld are investigated in the framework of thermodynamic geometry. A detailed analysis of the thermodynamics, stability and phase structures in the canonical and the grand canonical ensembles for these AdS braneworld black holes are described. The thermodynamic curvatures for both these AdS braneworld black holes are computed and studied as a function of the thermodynamic variables. Through this analysis we illustrate an interesting dependence of the phase structur…
In this paper, we consider a static black hole in $f(R)$ gravity. We recapitulate the expression for corrected thermodynamic entropy of this black hole due to small fluctuations around equilibrium. Also, we study the geometrothermodynamics (GTD) of this black hole and investigate the adaptability of the curvature scalar of geothermodynamic methods with phase transition points of this black hole. Moreover, we study the effect of correction parameter on thermodynamic behaviour of this black hole. We observe that the singular point of the curvature scalar of Ruppeiner metric coincides completely …
Due to the asymptotic structure of the black hole solution, there are two different thermodynamic schemes for the charged Banados-Teitelboim-Zanelli (BTZ) black hole. In one scheme, the charged BTZ black hole is super-entropic, while in the other, it is not (the reverse isoperimetric inequality is saturated). In this paper, we investigate the thermodynamic curvature of the charged BTZ black hole in different coordinate spaces. We find that in both schemes, the thermodynamic curvature is always positive, which may be related to the information of repulsive interaction between black hole molecul…
Lorentz-violating gravity theories with a preferred foliation can have instantaneous propagation. Nonetheless, it has been shown that black holes can still exist in such theories and the relevant notion of an event horizon has been dubbed `universal horizon'. In stationary spacetimes the universal horizon has to reside in a region of spacetime where the Killing vector associated with stationarity is spacelike. This raises the question of what happens to the universal horizon in the extremal limit, where no such region exists anymore. We use a decoupling limit approximation to study this proble…
In black hole thermodynamics of certain models, the thermodynamic first law may contain the pressure term. The corresponding entropy follows the area law whereas the thermodynamic energy is not the same with the black hole mass. If the pressure can be decomposed into two parts and recombined with the original thermodynamic quantities, then the thermodynamic energy becomes the black hole mass and the entropy satisfying the area law turns out to be the corrected entropy called the Wald entropy, respectively.
Recently we have shown [1604.08812] how to formulate a thermodynamic first law for a single (charged) accelerated black hole in AdS space by fixing the conical deficit angles present in the spacetime. Here we show how to generalise this result, formulating thermodynamics for black holes with varying conical deficits. We derive a new potential for the varying tension defects: the "thermodynamic length", both for accelerating and static black holes. We discuss possible physical processes in which the tension of a string ending on a black hole might vary, and also map out the thermodynamic phase …
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…
The thermodynamic geometry has been proved to be quite useful in understanding the microscopic structure of black holes. We investigate the phase structure, thermodynamic geometry and critical behavior of a Reissner-Nordstrom-AdS black hole and a Reissner-Nordstrom black hole in a cavity, which can reach equilibrium in a canonical ensemble. Although the phase structure and critical behavior of both cases show striking resemblance, we find that there exist significant differences between the thermodynamic geometry of these two cases. Our results imply that there may be a connection between the …
In this paper, a preliminary correspondence between the thermodynamic curvature and the isoperimetric theorem is established from a $4$-dimensional ultraspinning black hole. We find that the thermodynamic curvature of ultraspinning black hole is negative which means the ultraspinning black hole is likely to present an attractive between its molecules phenomenologically if we accept the analogical observation that the thermodynamic curvature reflects the interaction between molecules in a black hole system. Meanwhile we obtain a general conclusion that the thermodynamic curvature of the extreme…
Thermodynamic relations for a class of 2D black holes are obtained corresponding to observations made from finite spatial distances. We also study the thermodynamics of the charged version of the Jackiw-Teitelboim black holes found recently by Lowe and Strominger. Our results corroborate, in appropriate limits, to those obtained previously by other methods. We also analyze the stability of these black holes thermodynamically.
Due to the non-independence of entropy and thermodynamic volume for spherically symmetric black holes in the AdS spacetime, when applying the Ruppeiner thermodynamic geometry theory to these black holes, we often encounter an unavoidable problem of the singularity about the line element of thermodynamic geometry. In this paper, we propose a basic and natural scheme for dealing with the thermodynamic geometry of spherically symmetric AdS black holes. We point out that enthalpy, not internal energy, is the fundamental thermodynamic characteristic function for the Ruppeiner thermodynamic geometry…
We obtain an exact slowly rotating Einstein-bumblebee black hole solution by solving the corresponding $rr$ and $tϕ$ components of the gravitational field equations in both cases: A, $b_μ=(0,b(r),0,0)$; B, $b_μ=(0,b(r),\mathfrak{b}(θ),0)$. Then we check the other gravitational field equations and the bumblebee field motion equations by using this solution. We find that in the case A, there exists a slowly rotating black hole solution indeed for arbitrary LV (Lorentz violation) coupling constant $\ell$; however as in the case B, there exists this slowly rotating solution if and only if the coup…
We study thermodynamic and classical instability of AdS black holes in fourth-order gravity. These include the BTZ black hole in new massive gravity, Schwarzschild-AdS black hole, and higher-dimensional AdS black holes in fourth-order gravity. All thermodynamic quantities which are computed using the Abbot-Deser-Tekin method are used to study thermodynamic instability of AdS black holes. On the other hand, we investigate the $s$-mode Gregory-Laflamme instability of the massive graviton propagating around the AdS black holes. We establish the connection between the thermodynamic instability and…
We consider the stability of black holes within both classical general relativity and the semiclassical thermodynamic description. In particular, we study linearised perturbations and their contribution to the gravitational partition function, addressing technical issues for charged (Reissner-Nordstrom) and rotating (Kerr-AdS) black holes. Exploring the connection between classical and thermodynamic stability, we find classical instabilities of Myers-Perry black holes and bifurcations to new black hole families.
One of the most striking evidences of the information loss paradox is that, according to the Hawking's calculation, the correlation functions of a test scalar field exponentially decay in time. In this paper, I argue that a judicious use of the steepest descent expansion on the classical saddle point (the Black Hole background), is enough to change this early time decay into a late time growing, in agreement with information retrieval. I will explicitly show this in the Jackiw-Teitelboim gravity. There, the so-called "ramp" in the bulk tow-point function, is analytically obtained without the n…
