继 H. Ellis 的工作之后，我们研究了 Schwarzschild 黑洞引力场中的曲速引擎。我们发现，只要曲速引擎以亚光速穿过黑洞视界，视界在曲速气泡内部就会有效消失。此外，我们发现黑洞的引力场能够缓解对弱能量条件（WEC）和零能量条件（NEC）的违反，从而减少维持曲速引擎所需的负能量，这可能有助于在实验室实验中制造微观曲速引擎。我们还考虑了与黑洞相互作用的曲速气泡的热力学，并指出了一些悖论，这些悖论可能表明我们从热力学角度对它们的理解存在空白。
英文摘要：
Following the work of H. Ellis, we study warp drives in the gravitational field of a Schwarzschild black hole. We find that as long as the warp drive crosses the black hole horizon at a subluminal speed, the horizon would be effectively absent inside the warp bubble. Moreover, we discover that the black hole's gravitational field can alleviate the violations of the weak energy condition (WEC) and the null energy condition (NEC) and therefore decrease the amount of negative energy required to sustain a warp drive, which may be instrumental for creating microscopic warp drives in lab experiments. We also consider the thermodynamics of a warp bubble interacting with a black hole and point out some paradoxes that may indicate a gap in our understanding of them from the thermodynamic point of view.
We have studied the quasinormal modes of a massive scalar field coupling to Einstein's tensor in the spacelike stretched $AdS_3$ black hole spacetime. We find that both the right-moving and left-moving quasinormal frequencies depend not only on the warped parameter $v$ of black hole, but also on the coupling between the scalar field and Einstein's tensor. Moreover, we also discuss the warped $AdS/CFT$ correspondence from the quasinormal modes and probe the effects of the coupling on the left and right conformal weights $h_L$ and $h_R$ of the operators dual to the scalar field in the boundary.
We study a possible amplification mechanism for the curvature perturbations generated during inflation by a Dirac-Born-Infeld (DBI) inflaton in the presence of a sharp feature in the warp factor. The large growth resulting in the scalar power spectrum is a consequence of the decreasing speed of sound. We obtain analytical approximate expressions for the relevant dynamical quantities both in the slow roll phase and during the transient phase which leads to the amplification. We finally compare our approximations to the exact numerical evolution and give, in such a context, the general rules for…
We study the Complexity=Volume conjecture for Warped AdS$_3$ black holes. We compute the spatial volume of the Einstein-Rosen bridge and we find that its growth rate is proportional to the Hawking temperature times the Bekenstein-Hawking entropy. This is consistent with expectations about computational complexity in the boundary theory.
We investigate stationary, rotationally symmetric solutions of a recently proposed three-dimensional theory of massive gravity. Along with BTZ black holes, we also obtain warped AdS_3 black holes, and (for a critical value of the cosmological constant) AdS_2 x S^1 as solutions. The entropy, mass and angular momentum of these black holes are computed.
We consider the various perturbations of self-dual warped AdS$_3$ black hole and obtain the exact expressions of quasinormal modes by imposing the vanishing Dirichlet boundary condition at asymptotic infinity. It is expected that the quasinormal modes agree with the poles of retarded Green's functions of the dual CFT. Our results provide a quantitative test of the warped AdS/CFT correspondence.
We investigate the stability of the horizon in a warped anti-de Sitter black hole based on the three-dimensional new massive gravity by particle absorption. If a particle moving towards the black hole enters its outer horizon, the black hole changes because it absorbs conserved quantities of the particle. This variation is constrained by the equations of motion for the particle. We prove both the irreducibility of the entropy and stability of the horizon for the black hole through this process. However, the instability of the horizon is found in a near-extremal black hole by considering its se…
We propose a set of diffeomorphism that act non-trivially near the horizon of the Kerr black hole. We follow the recent developments of Haco-Hawking-Perry-Strominger to quantify this phase space, with the most substantial difference being our choice of vectors fields. Our gravitational charges are organized into a Virasoro-Kac-Moody algebra with non-trivial central extensions. We interpret this algebra as arising from a warped conformal field theory. Using the data we can infer from this warped CFT description, we capture the thermodynamic properties of the Kerr black hole.
In this paper, we analytically calculate the quasinormal modes of scalar, vector, tensor, and spinor perturbations of the warped dS$_3$ black hole. There are two horizons for the warped dS$_3$ black hole, namely, the black hole horizon $r_b$ and the cosmological horizon $r_c$. In the calculation, we impose the ingoing boundary condition at the black hole horizon and the outgoing boundary condition at the cosmological horizon. We also investigate the hidden conformal symmetry of the warped dS$_3$ black hole in the region between the black hole horizon and the cosmological horizon $r_b<r<r_c$. W…
We construct a stretched (aka Warped) Anti-de Sitter black hole in 3 dimensions supported by a real scalar field configuration. The latter is regular everywhere outside and on the horizon. No hair theorems in 3 dimensions demand the matter to be coupled to the curvature in a non-minimal way; however, this coupling can still be of the Horndeski type, i.e. yielding second order field equations similar to those appearing in the context of Galileon theories. These Warped-Anti-de Sitter black holes exhibit interesting thermodynamical properties, such as finite Hawking temperature and entropy. We co…
We consider a black hole solution whose spatial boundary is a squashed three sphere in Einstein gravity with negative cosmological constant. We solve the Einstein equations numerically and find a warped AdS black hole solution with arbitrary squashing parameter. This solution becomes the ordinary AdS-Schwarzschild solution when the squashing parameter is chosen appropriately. Motivated by this fact, we study N=4 super Yang-Mills theory with zero coupling constant on a squashed three sphere and show that the thermodynamical entropy of this theory roughly agrees with that of the warped AdS black…
We demonstrate that the warped AdS3 black hole solutions of Topologically Massive Gravity are classically stable against massive scalar field perturbations by analysing the quasinormal and bound state modes of the scalar field. In particular, it is found that although classical superradiance is present it does not give rise to superradiant instabilities. The stability is shown to persist even when the black hole is enclosed by a stationary mirror with Dirichlet boundary conditions. This is a surprising result in view of the similarity between the causal structure of the warped AdS3 black hole …
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…
We first review spacelike stretched warped AdS$_3$ and we describe its black hole quotients by using accelerating and Poincaré coordinates. We then describe the maximal analytic extension of the black holes and present their causal diagrams. Finally, we calculate spacetime limits of the black hole phase space $(T_R,T_L)$. This is done by requiring that the identification vector $\partial_θ$ has a finite non-zero limit. The limits we obtain are the self-dual solution in accelerating or Poincaré coordinates, depending respectively on whether the limiting spacetimes are non-extremal or extremal, …
We apply the warped product spacetime scheme to the Banados-Teitelboim-Zanelli black holes and the Reissner-Nordström-anti-de Sitter black hole to investigate their interior solutions in terms of warped products. It is shown that there exist no discontinuities of the Ricci and Einstein curvatures across event horizons of these black holes.
The absorption cross section is studied in the low-frequency region for a propagating scalar field under the warped AdS$_3$ black hole background in the topologically massive gravity. It can be shown that the absorption cross section is significantly deformed by the gravitational Chern-Simons term, which is proportional to the scattering area of black hole with an additional contribution depending on the left-moving and right-moving temperatures. It means that the cross section is larger than the area in spite of the s-wave limit. Finally, we discuss the left-right quasinormal modes for the sc…
Exploiting a multiply warped product manifold scheme, we study the interior solutions of the Banados-Teitelboim-Zanelli black holes and the exterior solutions of the de Sitter black holes in the (2+1) dimensions.
We investigate the asymptotic structure of the three dimensional warped anti de sitter black holes in the Bergshoeff, Hohm and Townsend massive gravity using the canonical Hamiltonian formalism. We define the canonical asymptotic guage generators, which produce the conserved charges and the asymptotic symmetry group for the warped anti de sitter black holes. The attained symmetry group is described by a semi direct sum of a Virasoro and a KacMoody algebra. Using the Sugawara construction, we obtain a direct sum of two Virasoro algebras. We show that not only the asymptotic conserved charges sa…
We study regular spacelike warped black holes in the three dimensional general massive gravity model, which contains both the gravitational Chern-Simons term and the linear combination of curvature squared terms characterizing the new massive gravity besides the Einstein-Hilbert term. The parameters of the metric are found by solving a quartic equation constrained by an inequality that imposes the absence of closed timelike curves. Explicit expressions for the central charges are suggested by exploiting the fact that these black holes are discrete quotients of spacelike warped AdS(3) and a kno…
The statistical entropy of a scalar field on the warped AdS$_3$ black hole in the cosmological topologically massive gravity is calculated based on the brick-wall method, which is different from the Wald's entropy formula giving the modified area law due to the higher-derivative corrections in that the entropy still satisfies the area law. It means that the entropy for scalar excitations on this background is independent of higher-order derivative terms or the conventional brick wall method has some limitations to take into account the higher-derivative terms.
We extend the recently proposal of hidden conformal symmetry to the self-dual warped AdS$_3$ black holes in topological massive gravity. It is shown that the wave equation of massive scalar field with sufficient small angular momentum can be reproduced by the SL(2, R) Casimir quadratic operator. Due to the periodic identification in the $ϕ$ direction, it is found that only the left section of hidden conformal symmetry is broken to U(1), while the right section is unbroken, which only gives the left temperature of dual CFT. As a check of the dual CFT conjecture of self-warped AdS$_3$ black hole…
We investigate the Dirac particles tunnelling as a radiation of Warped AdS$_{3}$ black hole family in Topological Massive Gravity. Using the Hamilton-Jacobi method, we discuss tunnelling probability and Hawking temperature of the spin-1/2 particles for the black hole and its extremal cases. We observe that the Hawking temperature of the non-extremal black hole higher than the extremal black hole when $ω<\frac{2\ r_{0}}{3}$, because the non-extremal black hole become unstable in this case.
We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u(1) current algebras and recover the surprisingly simple entropy formula $S=2π(J_0^+ + J_0^-)$, where $J_0^\pm$ are zero mode charges of the current algebras. This provides the first example of a locally non-m…
The belief still persists, at least for an important part of the community, that in general relativity the cosmological constant $Λ$ must remain immaculate. However, Bianchi identities show that $Λ$ could acquire local properties in the presence of matter, i.e., $Λ\rightarrow\,Λ(x^μ)$. In this paper we go even further, and we show that a non-uniform vacuum energy does not even require coexistence with any additional form of matter-energy, nor of any theory beyond general relativity, at least for extreme environments, such as the proximity of a black hole.
In this letter, we provide an alternative method to study the area spectrum of certain classes of extremal black holes which have near-horizon geometry as warped AdS. We argue that previous methods which are based on the existence of quasinormal modes may not be applicable in the extremal limit. The topology difference of the near-horizon geometry between non-extremal and extremal black holes implies a separate treatment is needed to study the area discreteness in the extremal limit. To be specific, we will study area spectrum of supersymmetric BMPV black holes/black rings and Reissner-Norstro…
We study the normal modes of a scalar field in the background of a warped AdS_3 black hole which arises in topologically massive gravity. We discuss the normal mode spectrum using the brick wall boundary condition. In addition, we investigate the possibility of a more general boundary condition for the scalar field.
In this paper we present the results of our analysis of the growth and decay of black holes possibly produced at the Large Hadron Collider, based on our previous study of black holes in the context of the warped brane-world scenario. The black hole mass accretion and decay is obtained as a function of time, and the maximum black hole mass is obtained as a function of a critical mass parameter. The latter occurs in our expression for the luminosity and is related to the size of extra-dimensional corrections to Newton's law. Based on this analysis, we argue against the possibility of catastrophi…
We study the static, analytical solution of black holes in the warped DGP braneworld scenario. We show that the linearized field equations and matching conditions lead to solutions that are not compatible with Schwarzschild-(A)dS$_{(4)}$ solutions on the brane. This incompatibility is similar to vDVZ discontinuity in massive gravity theory. Following the standard procedure to remove this discontinuity, which firstly was proposed by Vainshtein, we keep some appropriate nonlinear terms in the field equations. This strategy has its origin in the fact that the spatial extrinsic curvature of the br…
Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological constant are considered in the case of spacelike stretched warping, where black holes have been shown to exist. We provide a set of asymptotic conditions that accommodate solutions in which the local degree of freedom (the "massive graviton") is switched on. An exact solution with this property is explicitly exhibited and possesses a slower fall-off than the warped AdS black hole. The boundary conditions are invariant under the semidirect product of the Virasoro algebra with a u(1) current algebra.…
Warped AdS$_3$ black hole thermodynamics and the charged Cardy formula
Sofia University（索非亚大学）；INRNE, Bulgarian Academy of Sciences（保加利亚科学院核物理与核能研究所）；Università di Modena e Reggio Emilia（摩德纳和雷焦艾米利亚大学）；INFN Sezione di Bologna（意大利国家核物理研究所博洛尼部分所）
In this paper we consider the warped AdS$_{3}$ black hole solution of topologically massive gravity with a negative cosmological constant, and we investigate the possibility that it acts as a particle accelerator by analyzing the energy in the center of mass (CM) frame of two colliding particles in the vicinity of its horizon, which is known as the Bañados, Silk and West (BSW) process. Mainly, we show that the critical angular momentum $(L_c)$ of the particle decreases when the parameter that controls the stretching deformation ($ν$) increases. Also, we show that despite the particle with $L_c…
We investigate aspects of the four-dimensional effective description of brane world scenarios based on warped compactification on anti-de Sitter space. The low-energy dynamics is described by visible matter gravitationally coupled to a ``dark'' conformal field theory. We give the linearized description of the 4d stress tensor corresponding to an arbitrary 5d matter distribution. In particular a 5d falling particle corresponds to a 4d expanding shell, giving a 4d interpretation of a trajectory that misses a black hole only by moving in the fifth dimension. Breakdown of the effective description…
The Alcubierre warp drive is an exotic solution in general relativity. It allows for superluminal travel at the cost of enormous amounts of matter with negative mass density. For this reason, the Alcubierre warp drive has been widely considered unphysical. In this study, we develop a model of a general warp drive spacetime in classical relativity that encloses all existing warp drive definitions and allows for new metrics without the most serious issues present in the Alcubierre solution. We present the first general model for subluminal positive-energy, spherically symmetric warp drives; cons…
"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other things, to precisely formulate the notion of "superluminal" communication. We verify the non-perturbative violation of the classical energy conditions of the Alcubierre and Natario warp drive spacetimes and apply linearized gravity to the weak-field warp drive, testing the energy conditions to first and second order of the non-relativistic warp-bubble velocity. We are primarily interested in a secondary feature of the warp drive that has not previously b…
Black holes in X-ray binaries are often assumed to be rotating perpendicular to the plane of the accretion disk and parallel to the orbital plane of the binary. While the Bardeen-Petterson effect forces the inner part of the accretion disk to be aligned with the equatorial plane of a spinning black hole, the disk may be warped such that the inclination angle of the outer part is different from that of the inner part. In this paper, we identify a possible observational signature of a warped accretion disk in the spectrum of the polarization degree of the continuum. Such a signature would provid…
Hawking radiation (HR) of massive vector particles from a rotating Warped Anti-de Sitter black hole in 2+1 dimensions (WAdS$_{\text{3}}$BH) is studied in detail. The quantum tunneling approach with the Hamilton-Jacobi method (HJM) is applied in the Proca equation (PE), and we show that the radial function yields the tunneling rate of the outgoing particles. Comparing the result obtained with the Boltzmann factor, we satisfactorily reproduce the Hawking temperature (HT) of the WAdS$_{\text{3}}$BH.
We reinvestigate the thermodynamics of black objects (holes and strings) in four-dimensional braneworld models that are originally constructed by Emparan, Horowitz and Myers based on the anti-de Sitter (AdS) C-metric. After proving the uniqueness of slicing the AdS C-metric, we derive thermodynamic quantities of the black objects by means of the Euclidean formulation and find that we have no necessity of requiring any regularization to calculate their classical action. We show that there exist the Bekenstein-Hawking law and the thermodynamic first law. The thermodynamic mass of the localized b…
It will be shown that while horizons do not exist for warp drive spacetimes traveling at subluminal velocities horizons begin to develop when a warp drive spacetime reaches luminal velocities. However it will be shown that the control region of a warp drive ship lie within the portion of the warped region that is still causally connected to the ship even at superluminal velocities, therefore allowing a ship to slow to subluminal velocities. Further it is shown that the warped regions which are causally disconnected from a warp ship have no correlation to the ship velocity.
A thorough investigation is presented of the exact black hole solution on a warped five-dimensional spacetime in conformal dilaton gravity (CDG), found in earlier work. Summarized, we will prove: The black hole solution in the CDG model on a warped 5D spacetime: 1. It is an exact solution for the metric components as well as for the dilaton field. 2.The quintic polynomial describing the zero's of the model, has no essential singularities. 3.If we write $^{(5)}g_{μν}=ω^{4/3}{^{(5)}}{\tilde g_{μν}}, ^{(5)}\tilde g_{μν}=^{(4)}\tilde g_{μν}+n_μn_ν, ^{(4)}\tilde g_{μν}=\barω^2 {^{(4)}}\bar g{μν}$ t…
In this work we analyse the potential for a warp drive spacetime to develop instabilities due to the presence of quantum matter. Particularly, we look for points of infinite blueshift (which are analogous to points of a black hole inner horizon, known for its semiclassical instability), and categorise them through the behaviour of geodesics in their vicinity. We find that warp-drive bubbles in dimension 2+1 or higher are in fact likely to be stable, as they generally contain only isolated points where divergences are approached, leading to a finite limit for the overall accumulation of destabi…
It is commonly believed that Alcubierre's warp drive works by contracting space in front of the warp bubble and expanding space behind it. We show that this expansion/contraction is but a marginal consequence of the choice made by Alcubierre, and explicitly construct a similar spacetime where no contraction/expansion occurs. Global and optical properties of warp drive spacetimes are also discussed.
A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natario warp drives at a constant velocity.Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes such as warp drives. Warp drives are the theoretical solutions to Einstein's field equations that allow the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is une…
To gain more insights about what could be the source of the Alcubierre warp drive, a technique designed to find an orthogonal basis from the metric expression is used. It is deduced that exotic fluids can produce the same stress-energy tensor as the Alcubierre warp drive. For different configurations of warp acceleration and velocity, constraints on density, pressure, total positive mass, total negative mass, absolute value of the equation of state as well as null-energy condition violation are provided. The Alcubierre warp drive Einstein tensor expression and the optimization of fluid propert…
In this paper we apply the thermodynamics method to investigate the holographic pictures for the BTZ black hole, the spacelike and the null warped black holes in three-dimensional topologically massive gravity (TMG) and new massive gravity (NMG). Even though there are higher derivative terms in these theories, the thermodynamics method is still effective. It gives consistent results with the ones obtained by using asymptotical symmetry group (ASG) analysis. In doing the ASG analysis we develop a brute-force realization of the Barnich-Brandt-Compere formalism with Mathematica code, which also a…
''Warp drive'' spacetimes are useful as ''gedanken-experiments'' and as a theoretician's probe of the foundations of general relativity. Applying linearized gravity to the weak-field warp drive, i.e., for non-relativistic warp-bubble velocities, we find that the occurrence of energy condition violations in this class of spacetimes is generic to the form of the geometry under consideration and is not simply a side-effect of the ''superluminal'' properties. Using the linearized construction it is now possible to compare the warp field energy with the mass-energy of the spaceship, and applying th…
A process for using curvature invariants is applied to evaluate the accelerating Natario warp drive. Curvature invariants are independent of coordinate bases and plotting the invariants is free of coordinate mapping distortions. While previous works focus mainly on the mathematical description of the warp bubble, plotting curvature invariants provides a novel pathway to investigate the Natário spacetime and its characteristics. For warp drive spacetimes, there are four independent curvature invariants the Ricci scalar, r_1, r_2, and w_2. The invariant plots demonstrate how each curvature invar…
We find a class of warp drive spacetimes possessing Newtonian limits, which we then determine. The same method is used to compute Newtonian limits of the Schwarzschild solution and spatially flat Friedmann-Robertson-Walker cosmological models.
