Schwarzschild-de Sitter Spacetime Research Articles

Thermodynamics of multi-horizon spacetimes

There exist several well-established procedures for computing thermodynamics for a single horizon spacetime. However, for a spacetime with multi-horizon, the thermodynamics is not very clear. It is not fully understood whether there exists a global temperature for the multi-horizon spacetime or not. Here we show that a global temperature can exist for Schwarzschild-de Sitter spacetime, Reissner-Nordstrom-de Sitter spacetime, and rotating BTZ black hole. This temperature does not coincide with the conventional Hawking temperature related to the outer horizon. We also show that the total entropy for these spacetimes can not be determined only by the outer horizon. The correlations between the horizons of these spacetimes determine it.

On the duality of Schwarzschild–de Sitter spacetime and moving mirror

The Schwarzschild–de Sitter (SdS) metric is the simplest spacetime solution in general relativity with both a black hole event horizon and a cosmological event horizon. Since the Schwarzschild metric is the most simple solution of Einstein’s equations with spherical symmetry and the de Sitter metric is the most simple solution of Einstein’s equations with a positive cosmological constant, the combination in the SdS metric defines an appropriate background geometry for semi-classical investigation of Hawking radiation with respect to past and future horizons. Generally, the black hole temperature is larger than that of the cosmological horizon, so there is heat flow from the smaller black hole horizon to the larger cosmological horizon, despite questions concerning the definition of the relative temperature of the black hole without a measurement by an observer sitting in an asymptotically flat spacetime. Here we investigate the accelerating boundary correspondence of the radiation in SdS spacetime without such a problem. We have solved for the boundary dynamics, energy flux and asymptotic particle spectrum. The distribution of particles is globally non-thermal while asymptotically the radiation reaches equilibrium.

Spacetime entanglement entropy of de Sitter and black hole horizons

We calculate Sorkin’s manifestly covariant entanglement entropy for a massive and massless minimally coupled free Gaussian scalar field for the de Sitter horizon and Schwarzschild de Sitter horizons, respectively, in d > 2. In de Sitter spacetime we restrict the Bunch–Davies vacuum in the conformal patch to the static patch to obtain a mixed state. The finiteness of the spatial norm in the static patch implies that is well defined for each mode. We find that for this mixed state is independent of the effective mass of the scalar field, and matches that of Higuchi and Yamamoto (2018 Phys. Rev. D 98 065014), where, a spatial density matrix was used to calculate the horizon entanglement entropy. Using a cut-off in the angular modes we show that , where A c is the area of the de Sitter cosmological horizon. Our analysis can be carried over to the black hole and cosmological horizon in Schwarzschild de Sitter spacetime, which also has finite spatial norm in the static regions. Although the explicit form of the modes is not known in this case, we use the boundary conditions of Qiu and Traschen (2020 Class. Quantum Grav. 37 135012) for a massless minimally coupled scalar field, to find the mode-wise , where b, c denote the black hole and de Sitter cosmological horizons, respectively. As in the de Sitter calculation we see that after taking a cut-off in the angular modes.

Horizons and correlation functions in 2D Schwarzschild-de Sitter spacetime

Two-dimensional Schwarzschild-de Sitter is a convenient spacetime in which to study the effects of horizons on quantum fields since the spacetime contains two horizons, and the wave equation for a massless minimally coupled scalar field can be solved exactly. The two-point correlation function of a massless scalar is computed in the Unruh state. It is found that the field correlations grow linearly in terms of a particular time coordinate that is good in the future development of the past horizons, and that the rate of growth is equal to the sum of the black hole plus cosmological surface gravities. This time dependence results from additive contributions of each horizon component of the past Cauchy surface that is used to define the state. The state becomes the Bunch-Davies vacuum in the cosmological far field limit. The two point function for the field velocities is also analyzed and a peak is found when one point is between the black hole and cosmological horizons and one point is outside the future cosmological horizon.

Accretion of matter and spectra of binary X-ray sources in massive gravity

We study low-mass binary X-ray sources involving stellar mass black holes within massive gravity. Regarding the accretion disk, we adopt the standard model for an optically thick, cool, and geometrically thin disk by Shakura–Sunyaev. For the gravitational field generated by the black hole, we consider the analogue of the Schwarzschild–de Sitter space–time of Einstein’s theory in massive gravity, for which we found an additional term linear in the radial coordinate. Then, we compute the radial velocity, the energy density and the pressure as a function of the radial coordinate, and the X-ray emission’s soft spectral component expected from the disk. We also investigated in detail the impact of this new geometry. Our result indicates that by using observed spectra from confirmed X-ray binaries involving astrophysical black holes, we can put strong constraints on alternative theories of gravity.

Optical functions in de Sitter

This paper addresses pure gauge questions in the study of asymptotically de Sitter spacetimes. We construct global solutions to the eikonal equation on de Sitter, whose level sets give rise to double null foliations, and give detailed estimates for the structure coefficients in this gauge. We show two results that are relevant for the foliations used by the author in the context of the stability problem of the expanding region of Schwarzschild de Sitter spacetimes: (i) Small perturbations of round spheres on the cosmological horizons lead to spheres that pinch off at infinity. (ii) Globally well-behaved double null foliations can be constructed from infinity using a choice of spheres related to the level sets of a new mass aspect function. While (i) shows that in the above stability problem a final gauge choice is necessary, the proof of (ii) already outlines a strategy for the case of spacetimes with decaying, instead of vanishing, conformal Weyl curvature.

Quasinormal modes for integer and half-integer spins within the large angular momentum limit

While independent observations have been made regarding the behaviour of effective quasinormal mode (QNM) potentials within the large angular momentum limit, we demonstrate analytically here that a uniform expression emerges for non-rotating, higher-dimensional, and spherically-symmetric black holes (BHs) in this regime for fields of integer and half-integer spin in asymptotically flat and dS BH contexts; a second uniform expression arises for these QNM potentials in AdS BH spacetimes. We then proceed with a numerical analysis based on the multipolar expansion method recently proposed by Dolan and Ottewill to determine the behaviour of quasinormal frequencies (QNF) for varying BH parameters in the eikonal limit. We perform a complete study of Dolan and Ottewill's method for perturbations of spin $s \in \{0,1/2,1,3/2,2 \}$ in 4D Schwarzschild, Reissner-Nordstr{\"o}m, and Schwarzschild de Sitter spacetimes, clarifying expressions and presenting expansions and results to higher orders $(\mathcal{O}(L^{-6}))$ than many of those presented in the literature $(\sim \mathcal{O}(L^{-2}))$. We find good agreement with known results of QNFs for low-lying modes; in the large-$\ell$ regime, our results are highly consistent with those of Konoplya's 6th-order WKB method. We confirm a universality in the trends of physical features recorded in the literature for the low-lying QNFs (that the real part grows indefinitely, the imaginary tends to a constant as $\ell \rightarrow \infty$, etc.) as we approach large values of $\ell$ within these spacetimes, and explore the consequent interplay between BH parameters and QNFs in the eikonal limit.

Path integrals for causal diamonds and the covariant entropy principle

We study causal diamonds in Minkowski, Schwarzschild, (anti) de Sitter, and Schwarzschild-de Sitter spacetimes using Euclidean methods. The null boundaries of causal diamonds are shown to map to isolated punctures in the Euclidean continuation of the parent manifold. Boundary terms around these punctures decrease the Euclidean action by $A_\diamond/4$, where $A_\diamond$ is the area of the holographic screen around the diamond. We identify these boundary contributions with the maximal entropy of gravitational degrees of freedom associated with the diamond.

Divergent part of the stress-energy tensor for Maxwell\u2019s theory in curved space-time: a systematic derivation

In this paper the Feynman Green function for Maxwell’s theory in curved space-time is studied by using the Fock–Schwinger–DeWitt asymptotic expansion; the point-splitting method is then applied, since it is a valuable tool for regularizing divergent observables. Among these, the stress-energy tensor is expressed in terms of second covariant derivatives of the Hadamard Green function, which is also closely linked to the effective action; therefore one obtains a series expansion for the stress-energy tensor. Its divergent part can be isolated, and a concise formula is here obtained: by dimensional analysis and combinatorics, there are two kinds of terms: quadratic in curvature tensors (Riemann, Ricci tensors and scalar curvature) and linear in their second covariant derivatives. This formula holds for every space-time metric; it is made even more explicit in the physically relevant particular cases of Ricci-flat and maximally symmetric spaces, and fully evaluated for some examples of physical interest: Kerr and Schwarzschild metrics and de Sitter space-time.

Black hole perturbations of massive and partially massless spin-2 fields in (anti) de Sitter spacetime

We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schrödinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with multipole number L = 1 in four spacetime dimensions, providing the explicit form of the underlying symmetry. We show that isospectrality between partially massless modes of different parity is broken in higher-dimensional Schwarzschild de Sitter spacetimes.

Kruskal-Szekeres coordinates of spherically symmetric solutions in theories of gravity

Understanding the missing matter problem in cosmological phenomena and scales of astrophysical is usually studied by modifying general relativity theory. In this article, we formulated the Kruskal-Szekeres coordinate of vacuum modified gravity model in f (R ) theory. The generalization of the field equation was obtained by generalizing Hilbert-Einstein’s action with gravitational Lagrangian in terms of f (r)function. By consider a special class of f(R) theory by taking R = R0 , we found the solution of static spherically symmetric spacetime that was known as de Sitter-Schwarzschild spacetime. The transformation rules were constructed from Kruskal-Szekeres coordinates in f (r)theory of modified general relativity to the Kruskal-Szekeres coordinate in general relativity theory. For λ ≈ 0, the Schwarzschild and Kruskal-Szekeres metric for static spherically symmetric on f (r)theory reduced to the standard Schwarzschild and Kruskal-Szekeres metric on general relativity. We also show the spacetime structure of de Sitter-Schwarzschild and Kruskal-Szekeres coordinate. This work could open a promising way to understand some features of a black hole in the f (r)theory of gravity.

Gravitational deflection of massive particles in Schwarzschild-de Sitter spacetime

In this paper, the gravitational deflection of a relativistic massive neutral particle in the Schwarzschild-de Sitter spacetime is studied via the Rindler–Ishak method in the weak-field limit. When the initial velocity v_0 of the particle tends to the speed of light, the result is consistent with that obtained in the previous work for the light-bending case. Our result is reduced to the Schwarzschild deflection angle of massive particles up to the second order, if the contributions from the cosmological constant varLambda are dropped. The observable correctional effects due to the deviation of v_0 from light speed on the varLambda -induced contributions to the deflection angle of light are also analyzed.

Schwarzschild de Sitter and extremal surfaces

We study extremal surfaces in the Schwarzschild de Sitter spacetime with real mass parameter. We find codim-2 timelike extremal surfaces stretching between the future and past boundaries that pass through the vicinity of the cosmological horizon in a certain limit. These are analogous to the surfaces in http://arxiv.org/abs/1711.01107 [hep-th]. We also find spacelike surfaces that never reach the future/past boundaries but stretch indefinitely through the extended Penrose diagram, passing through the vicinity of the cosmological and Schwarzschild horizons in a certain limit. Further, these exhibit interesting structure for de Sitter space (zero mass) as well as in the extremal, or Nariai, limit.

On the symmetry and conservation law classification of the de Sitter–Schwarzschild metric and the corresponding wave and Klein–Gordon equations

The main purpose of this work is to focus on a discussion of Lie symmetries admitted by de Sitter–Schwarzschild spacetime metric, and the corresponding wave or Klein–Gordon equations constructed in the de Sitter–Schwarzschild geometry. The obtained symmetries are classified and the variational (Noether) conservation laws associated with these symmetries via the natural Lagrangians are obtained. In the case of the metric, we obtain additional variational ones when compared with the Killing vectors leading to additional conservation laws and for the wave and Klein–Gordon equations, the variational symmetries involve less tedious calculations as far as invariance studies are concerned.

An exact black hole spacetime with scalar field and its shadow together with quasinormal modes

We find an exact black hole solution with a minimally coupled scalar field. The corresponding spacetime has two horizons and one of them is the black hole event horizon and the other is the cosmic horizon. In this sense, the solution is analogous to the Schwarzschild-de Sitter (or anti-de Sitter) spacetime. We investigate the thermodynamics and construct the first law of thermodynamics. At the same time, we make a study on the shadow and quasinormal modes of this black hole solution.

Stable, thin wall, negative mass bubbles in de Sitter space-time

Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Heretofore, only {\it configurations} of negative mass had been found \cite{Belletete:2013nqa,Mbarek:2014ppa}, the analysis did not address stability or dynamics. In this paper, we analyze both of these criteria. We demonstrate the existence of {\it stable}, static, negative mass bubbles in an asymptotically de Sitter space-time. The bubbles are solutions of the Einstein equations and correspond to an interior region of space-time containing a specific mass distribution, separated by a thin wall from the exact, negative mass Schwarzschild-de Sitter space-time in the exterior. We apply the Israel junction conditions at the wall. For the case of an interior corresponding simply to de Sitter space-time with a different cosmological constant from the outside space-time, separated by a thin wall with energy density that is independent of the radius, we find static but unstable solutions which satisfy the dominant energy condition everywhere. The bubbles can collapse through spherically symmetric configurations to the exact, singular, negative mass Schwarzschild-de Sitter solution. Interestingly, this provides a counter-example of the cosmic censorship hypothesis. Alternatively, the junction conditions can be used to give rise to an interior mass distribution that depends on the potential for the radius of the wall. We show that for no choice of the potential, for positive energy density on the wall that is independent of the radius, can we get a solution that is non-singular at the origin. However, if we allow the energy density on the wall to depend on the radius of the bubble, we can find {\it stable}, static, non-singular solutions of negative mass which everywhere satisfy the dominant energy condition.

Black holes, oscillating instantons and the Hawking-Moss transition

Static oscillating bounces in Schwarzschild de Sitter spacetime are investigated. The oscillating bounce with many oscillations gives a super-thick bubble wall, for which the total vacuum energy increases while the mass of the black hole decreases due to the conservation of Arnowitt-Deser-Misner (ADM) mass. We show that the transition rate of such an “up-tunneling” consuming the seed black hole is higher than that of the Hawking- Moss transition. The correspondence of analyses in the static and global coordinates in the Euclidean de Sitter space is also investigated.

On the Mass of Static Metrics with Positive Cosmological Constant: II

This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as the only static vacuum metric with zero mass. In this second part, we prove optimal area bounds for horizons of black hole type and of cosmological type, corresponding to Riemannian Penrose inequalities and to cosmological area bounds à la Boucher–Gibbons–Horowitz, respectively. Building on the related rigidity statements, we also deduce a uniqueness result for the Schwarzschild–de Sitter spacetime.

Galactic Rotation Curves in Conformal Scalar-Tensor Gravity

We show quantitatively that an exact solution of conformal scalar-tensor gravity can explain very well the galactic rotation curves for a sample of 104 galaxies without the need for dark matter or other exotic modification of gravity. The metric is an overall rescaling of the Schwarzschild-de Sitter space-time as required by Weyl conformal invariance, which has to be spontaneously broken, and the velocity of the stars depends only on two fixed universal parameters. Using the Monte Carlo Markov Chain (MCMC) method, we make a fit of the observational rotation curves in order to get the mass-to-light ratio for each galaxy. Finally, we analytically compare our model with the modified Newtonian dynamics (MOND) and the metric skew tensor gravity (MSTG) showing that the three theories have a very different behavior at very large distances.

Schottky anomaly of deSitter black holes

The interplay of black hole and cosmological horizons introduces distinctive thermodynamic behavior for deSitter black holes, including well-known upper bounds for the mass and entropy. We point to a new such feature, a Schottky peak in the heat capacity of Schwarzschild–deSitter (SdS) black holes. With this behavior in mind, we explore statistical models for the underlying quantum degrees of freedom of SdS holes. While a simple two-state spin model gives Schottky behavior, in order to capture the non-equilibrium nature of the SdS system we consider a system with a large number of non-interacting spins. We examine to what extent constrained states of this system reproduce the thermodynamic properties of the black hole. We also review results of a recent study of particle production in SdS spacetimes in light of the Schottky anomaly and our spin models.