Usual Schwarzschild Research Articles

Minimum measurable length inspired thermodynamic characteristics of the Schwarzschild black hole surrounded by the cloud of strings and quintessence

We explore the thermodynamic properties of the Schwarzschild black hole surrounded by quintessence matter and a cloud of strings within the framework of the generalized Heisenberg algebra. We provide precise computations of temperature, heat capacity, and entropy associated with this black hole and investigate the impacts of various deformations of the Heisenberg algebra on these thermodynamic parameters. The findings are compared with those for the usual Schwarzschild black hole. Additionally, the behavior of the isotherm related to this black hole is studied. It is anticipated that remnants will hold the key to solving the information loss problem. It is observed that different deformations of the Heisenberg algebra, which introduce minimum measurable length, maximum measurable momenta, or both simultaneously, could lead to the existence of a black hole remnant. Furthermore, it is noted that both exotic fields, cloud of strings and quintessence contribute to the quantum gravity-corrected entropy of the composite system.

Physical analysis of matter accretion and evaporation of holographic massive gravity black hole

We study the matter accretion process onto Schwarzschild black hole in holographic massive gravity and investigate the impact of massive gravitons R and C on the accretion. Using the dynamical approach, we find out the nature of accretion for well known fluids such as ultra-stiff fluid, ultra-relativistic fluid, radiation fluid and sub-relativistic fluid. We discuss the accretion for polytropic fluid and evaluate the mass rate for the Schwarzschild black hole in holographic massive gravity. We also study the evaporation of Schwarzschild AdS black hole in holographic massive gravity. We analyze that initially black hole losses mass quickly, then evaporation process becomes slower and small black hole requires infinite time to evaporate which mean that black hole becomes remnant and third law of black hole thermodynamics satisfies. We observe that massive gravitons R and C have significant impact on the accretion process and Schwarzschild AdS black hole evaporates more quickly in holographic massive gravity as compare to usual Schwarzschild AdS black hole.

Thermodynamics of a modified Schwarzschild white hole in the presence of a cosmological constant

In this paper, we modify the usual Schwarzschild white hole in the presence of the cosmological constant. We then study its [Formula: see text] criticality, heat capacity, derive its equation of state, and then its stability conditions. In the process, we find that the thermal properties of the modified Schwarzschild white hole are not that of the usual Schwarzschild white hole as first stated in the literature by Stephen Hawking and then confirmed by others, but in fact, they are analogous to the thermal properties of our the universe.

Suppression of lithium depletion in young low-mass stars from fast rotation

We compute rotating 1D stellar evolution models that include a modified temperature gradient in convection zones and criterion for convective instability inspired by rotating 3D hydrodynamical simulations performed with the MUSIC code. In those 3D simulations we found that convective properties strongly depend on the Solberg–Høiland criterion for stability. We therefore incorporated this into 1D stellar evolution models by replacing the usual Schwarzschild criterion for stability and also modifying the temperature gradient in convection zones. We computed a grid of 1D models between 0.55 and 1.2 stellar masses from the pre-main sequence to the end of main sequence in order to study the problem of lithium depletion in low-mass main sequence stars. This is an ideal test case because many of those stars are born as fast rotators and the rate of lithium depletion is very sensitive to the changes in the stellar structure. Additionally, observations show a correlation between slow rotation and lithium depletion, contrary to expectations from standard models of rotationally driven mixing. By suppressing convection, and therefore decreasing the temperature at the base of the convective envelope, lithium burning is strongly quenched in our rapidly rotating models to an extent sufficient to account for the lithium spread observed in young open clusters.

ISCOs and OSCOs in the Presence of a Positive Cosmological Constant in Massive Gravity

We study the impact of a non-vanishing (positive) cosmological constant on the innermost and outermost stable circular orbits (ISCOs and OSCOs, respectively) within massive gravity in four dimensions. The gravitational field generated by a point-like object within this theory is known, generalizing the usual Schwarzschild–de Sitter geometry of General Relativity. In the non-relativistic limit, the gravitational potential differs by the one corresponding to the Schwarzschild–de Sitter geometry by a term that is linear in the radial coordinate with some prefactor γ, which is the only free parameter. Starting from the geodesic equations for massive test particles and the corresponding effective potential, we obtain a polynomial of fifth order that allows us to compute the innermost and outermost stable circular orbits. Next, we numerically compute the real and positive roots of the polynomial for several different structures (from the hydrogen atom to stars and globular clusters to galaxies and galaxy clusters) considering three distinct values of the parameter γ, determined using physical considerations, such as galaxy rotation curves and orbital precession. Similarly to the Kottler spacetime, both ISCOs and OSCOs appear. Their astrophysical relevance as well as the comparison with the Kottler spacetime are briefly discussed.

Image of a regular phantom compact object and its luminosity under spherical accretions

We have studied the shadow and its luminosity for a static and regular phantom compact object under the static spherical accretion and the infalling spherical accretion, respectively. Comparing with the usual Schwarzschild black hole, the presence of phantom hair yields the larger black hole shadow and the darker image. In both spherical accretion models, with the increase of phantom parameter, the maximum luminosity occurred at photon ring and the brightness of the central region in the shadow decrease, but in the region far from the shadow, the luminosity of image slightly increases. The image of a phantom wormhole and its luminosity have similar behaviors. Moreover, as the phantom charge parameter α increases up to the critical value at where the compact object changes from black hole to wormhole, there exists a jump for the specific intensity, which also appears in the slowly rotating case. This implies that the phantom hair is imprinted on both the shadow radius and the intensity of the electromagnetic flux radiation around compacted object.

Black hole scalarization in Gauss-Bonnet extended Starobinsky gravity

We propose a class of higher-derivative gravities that can be viewed as the Gauss-Bonnet extension of the Starobinsky model. The theory admits the Minkowski spacetime vacuum whose linear spectrum consists of the graviton and a massive scalar mode. In addition to the usual Schwarzschild black hole, we use numerical analysis to establish that in some suitable mass range, new black holes carrying the massive scalar hair can emerge. The new black hole serves as a "wall" separating the naked spacetime singularity and wormholes in the parameter space of the scalar hair. Our numerical results also indicate that although the new hairy black hole and the Schwarzschild have different spacetime geometry, their entropy and temperature are same for the same mass.

Modified Schwarzschild metric from a unitary accelerating mirror analog

We present a modified Schwarzschild solution for a model of evaporation of a black hole with information preservation. By drawing a direct analogy to the quantum pure accelerating mirror (dynamical Casimir effect of a 1D horizon), we derive a Schwarzschild metric with not only the usual Schwarzschild radius but an additional length scale related to the Planck length. The black hole has thermal particle production that leads to complete evaporation of the black hole, resulting in non-divergent entanglement entropy, Page curve turn-over, and an asymptotic quantum pure state with no information loss.

Phenomenology of GUP stars

We study quantum corrections at the horizon scale of a black hole induced by a Generalized Uncertainty Principle (GUP) with a quadratic term in the momentum. The interplay between quantum mechanics and gravity manifests itself into a non-zero uncertainty in the location of the black hole radius, which turns out to be larger than the usual Schwarzschild radius. We interpret such an effect as a correction which makes the horizon disappear, as it happens in other models of quantum black holes already considered in literature. We name this kind of horizonless compact objects GUP stars. We also investigate some phenomenological aspects in the astrophysical context of binary systems and gravitational wave emission by discussing Love numbers, quasi-normal modes and echoes, and studying their behavior as functions of the GUP deformation parameter. Finally, we preliminarily explore the possibility to constrain such a parameter with future astrophysical experiments.

Thin accretion disk around the distorted Schwarzschild black hole

We construct the relativistic standard steady, optically thick, cold and geometrically thin accretion disk around a distorted Schwarzschild black hole. The distortion of this static and axially symmetric black hole solution, is connected to an external distribution of matter. If the effects due to the rotation are negligible, this distribution can describe the exterior of any axially symmetric astrophysical model. Also, the distortion could be related to the outer parts of the accretion disk. We study the effects due to a distortion up to the quadrupole, and compare the physical characteristics of this disk to the usual Schwarzschild case.

Thermodynamics and its quantum correction of non-commutative Schwarichild black hole

Black hole thermodynamics establishes a deep and satisfying link to gravity, thermodynamics, and quantum theory. And, the thermodynamic property of black hole is essentially a quantum feature of gravity. In this paper, in order to study the influence of the quantum gravity effect on the quantum properties of black hole, we study the thermodynamics and its quantum correction to a non-commutative black hole. First of all, the temperature of the non-commutative Schwarichild black hole is calculated by using three different methods: surface gravity, tunneling effects and the first law of black hole thermodynamics. It is found that the same hole temperature is obtained by means of the surface gravity and tunneling effects. However, by using the first law of black hole thermodynamics, different results are derived from the first two methods. Therefore, we incline to the result obtained by surface gravity and tunneling effects, and the temperature obtained by the thermodynamic law needs modifying. That is, for the non-commutative black hole, there is a contradiction to the first law of thermodynamics. To calculate the temperature and other thermodynamic quantities for the non-commutative Schwarichild black hole, we use the corrected first law of black hole thermodynamics proposed in the literature. It is found that the black hole temperature derived by the corrected first law is the same as the temperature obtained by the surface gravity and the tunneling model, and the black hole entropy still follows Beckenstein-Hawking area law. Also, the heat capacity of the black hole is obtained and analyzed. It is seen that when the horizon radius and non-commutative parameter satisfy the particular conditions, the heat capacity is positive and the non-commutative black holes are thermodynamically stable. This is a different result from that of the usual Schwarichild black hole. Further, by studying the influence of generalized uncertainty principle on non-commutative black hole thermodynamics, the quantum corrections from generalized uncertainty principle for temperature, entropy and heat capacity of the non-commutative Schwarzschild black hole are given. It is found that with considering this quantum gravity effect, the obtained black hole entropy contains the item of are alogarithm. If the effect of the generalized uncertainty principle is neglected, the corrected black hole entropy can return to that in the usual case of Beckenstein-Hawing area law. Similarly, the corrected black hole temperature and heat capacity can also return to their counterparts in the case of usual Schwarzschild black hole when this quantum gravity effect is ignored.

Classical Polymerization of the Schwarzschild Metric

We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a way that a transformation maps classical variables to their polymeric counterpart. We show that the usual Schwarzschild metric can be extracted from a Hamiltonian function which in turn gets modifications due to the classical polymerization. Then, the polymer corrected Schwarzschild metric may be obtained by solving the polymer-Hamiltonian equations of motion. It is shown that while the conventional Schwarzschild space-time is a vacuum solution of the Einstein equations, its polymer-corrected version corresponds to an energy-momentum tensor that exhibits the features of dark energy. We also use the resulting metric to investigate some thermodynamical quantities associated with the Schwarzschild black hole, and in comparison with the standard Schwarzschild metric the similarities and differences are discussed.

Phase transition of quantum-corrected Schwarzschild black hole in rainbow gravity

The thermodynamic phase transition of Schwarzschild black hole, after employing a quantum correction to the space–time metric, in the gravity's rainbow is explored. The rainbow gravity-inspired Hawking temperature of the quantum-corrected rainbow Schwarzschild black hole is calculated initially, and then the entropy, the local temperature, and the local energy of the black hole in an isothermal cavity are derived. The off-shell free energy is calculated to further investigate the critical behavior, the thermodynamic stability, and the phase transition of the black hole. It is evident that the rainbow gravity determines the late fate of the black hole as leading to a remnant, the findings of this letter also show that a quantum correction to the metric reduces the remnant mass of the Schwarzschild black hole in comparison with the usual rainbow Schwarzschild black hole.

Plausible black hole solutions in higher-derivative gravity

Here we obtain explicit black hole solutions in Extension Gravity models with high-order derivative terms, while the Lichnerowicz-type theorem simplifies our analysis by vanishing Ricci's scalar curvature. We find out two explicit static, spherical solutions that satisfy the presented action: the first one is the same usual Schwarzschild solution and the other one is the new non-Schwarzschild solution. It means that Schwarzschild's solution following the no-hair theorem can describe any black hole object on each gravity theory. Without considering the first law of thermodynamics for it, we show that the non-Schwarzschild solution is depending on its set of constants, and then we consider its entropy and other thermodynamic parameters for specific values of the constants. Dans le cadre de modèles de gravité étendue comportant des dérivées d'ordre supérieur, nous obtenons des solutions explicites représentant des trous noirs. Nous trouvons deux solutions sphériques statiques qui vérifient les équations : la première est la solution de Schwarzschild bien connue, alors que l'autre est une solution nouvelle non schwarzschildienne. Ainsi, la solution de Schwarzschild, qui résulte du théorème « sans cheveux », peut décrire un trou noir dans l'une ou l'autre des théories de la gravité. Sans partir de la première loi de la thermodynamique, nous montrons que la solution non schwarzschildienne dépend de certaines constantes, et nous évaluons son entropie et les autres grandeurs thermodynamiques pour des valeurs spécifiques des constantes.

Null geodesics and red–blue shifts of photons emitted from geodesic particles around a noncommutative black hole space–time

We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space–time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817

We study relativistic stars in degenerate higher-order scalar-tensor theories that evade the constraint on the speed of gravitational waves imposed by GW170817. It is shown that the exterior metric is given by the usual Schwarzschild solution if the lower order Horndeski terms are ignored in the Lagrangian and a shift symmetry is assumed. However, this class of theories exhibits partial breaking of Vainshtein screening in the stellar interior and thus modifies the structure of a star. Employing a simple concrete model, we show that for high-density stars the mass-radius relation is altered significantly even if the parameters are chosen so that only a tiny correction is expected in the Newtonian regime. We also find that, depending on the parameters, there is a maximum central density above which solutions cease to exist.

Exact derivation of the Hawking effect in canonical formulation

The Hawking effect is one of the most extensively studied topics in modern physics. Yet it remains relatively under-explored within the framework of canonical quantization. The key difficulty lies in the fact that the Hawking effect is principally understood using the relation between the ingoing modes which leave past null infinity and the outgoing modes which arrive at future null infinity. Naturally, these modes are described using advanced and retarded null coordinates instead of the usual Schwarzschild coordinates. However, null coordinates do not lead to a true Hamiltonian that describes the evolution of these modes. In order to overcome these hurdles in a canonical formulation, we introduce here a set of near-null coordinates which allows one to perform an exact Hamiltonian-based derivation of the Hawking effect. This derivation opens up an avenue to explore the Hawking effect using different canonical quantization methods such as polymer quantization.

Poincaré invariance and asymptotic flatness in shape dynamics

Shape dynamics is a theory of gravity that waives refoliation invariance in favor of spatial Weyl invariance. It is a canonical theory, constructed from a Hamiltonian, $3+1$ perspective. One of the main deficits of shape dynamics is that its Hamiltonian is only implicitly constructed as a functional of the phase space variables. In this paper, I write down the equations of motion for shape dynamics to show that over a curve in phase space representing a Minkowski space-time, shape dynamics possesses Poincar\'e symmetry for appropriate boundary conditions. The proper treatment of such boundary conditions leads us to completely formulate shape dynamics for open manifolds in the asymptotically flat case. We study the charges arising in this case and find a new definition of total energy, which is completely invariant under spatial Weyl transformations close to the boundary. We then use the equations of motion once again to find a nontrivial solution of shape dynamics, consisting of a flat static Universe with a pointlike mass at the center. We calculate its energy through the new formula and rederive the usual Schwarzschild mass.

Exact hairy black holes and their modification to the universal law of gravitation

In this paper two things are done. First, it is pointed out the existence of exact asymptotically flat, spherically symmetric black holes when a self interacting, minimally coupled scalar field is the source of the energy momentum of the Einstein equations in four dimensions. The scalar field potential is the recently found to be compatible with the hairy generalization of the Plebanski-Demianski solution of general relativity. This paper describes the spherically symmetric solutions that smoothly connect the Schwarzschild black hole with its hairy counterpart. The geometry and scalar field are everywhere regular except at the usual Schwarzschild like singularity inside the black hole. The scalar field energy momentum tensor satisfies the null energy condition in the static region of the spacetime. The first law holds when the parameters of the scalar field potential are fixed under thermodynamical variation. Secondly, it is shown that an extra, dimensionless parameter, present in the hairy solution, allows to modify the gravitational field of a spherically symmetric black hole in a remarkable way. When the dimensionless parameter is increased, the scalar field generates a flat gravitational potential, that however asymptotically matches the Schwarzschild gravitational field. Finally, it is shown that a positive cosmological constant can render the scalar field potential convex if the parameters are within a specific rank.

Black hole spectroscopy via adiabatic invariant in a quantum corrected spacetime

Using the modified Kunstatter method, which employs as proper frequency the imaginary part instead of the real part of the quasinormal modes, the entropy spectrum and area spectrum of the modified Schwarzschild black holes in gravity’s rainbow are investigated. In the current study, two cases of modified dispersion relations concerning energy dependent and energy independent speed of light are considered. The entropy spectra with equal spacing are derived in these two cases. Furthermore, the obtained entropy spectra are independent of the energy of a test particle and are the same as the one of the usual Schwarzschild black hole. Also, the same area spectrum formulas are obtained in these different dispersion relations. However, due to the quantum effect of spacetime, the obtained area spectra are not equally spaced and are different from the one of the usual Schwarzschild black hole. Besides, in these two cases, the same black hole entropy formulas with logarithmic correction to the standard Bekenstein–Hawking area formula are obtained by the adiabatic invariant. The form of area spacing formulas and entropy formulas are independent of the particle’s energy, but the area spacing and entropy can have energy dependence through the area.