Constraining the number of horizons with energy conditions

We show that the number of horizons of static black holes can be strongly constrained by energy conditions of matter fields. After a careful clarification on the ``interior'' of a black hole, we prove that if the interior of a static black hole satisfies strong energy condition or null energy condition, there is at most one non-degenerated inner Killing horizon behind the non-degenerated event horizon. Our result offers some universal restrictions on the number of horizons. Interestingly and importantly, it also suggests that matter not only promotes the formation of event horizon but also prevents the appearance of multiple horizons inside black holes. Furthermore, using the geometrical construction, we obtain a radially conserved quantity which is valid for general static spacetimes.

Black holes with topological charges in Chern-Simons AdS5 supergravity

We study static black hole solutions with locally spherical horizons coupled to non-Abelian field in $$ \mathcal{N} $$ N = 4 Chern-Simons AdS5 supergravity. They are governed by three parameters associated to the mass, axial torsion and amplitude of the internal soliton, and two ones to the gravitational hair. They describe geometries that can be a global AdS space, naked singularity or a (non-)extremal black hole. We analyze physical properties of two inequivalent asymptotically AdS solutions when the spatial section at radial infinity is either a 3-sphere or a projective 3-space. An important feature of these 3-parametric solutions is that they possess a topological structure including two SU(2) solitons that wind nontrivially around the black hole horizon, as characterized by the Pontryagin index. In the extremal black hole limit, the solitons’ strengths match and a soliton-antisoliton system unwinds. That limit admits both non-BPS and BPS configurations. For the latter, the pure gauge and non-pure gauge solutions preserve 1/2 and 1/16 of the original supersymmetries, respectively. In a general case, we compute conserved charges in Hamiltonian formalism, finding many similarities with standard supergravity black holes.

Probing the parameters of a Schwarzschild black hole surrounded by quintessence and cloud of strings through four standard astrophysical tests

In this paper, we concern about applying general relativistic tests on the spacetime produced by a static black hole associated with cloud of strings, in a universe filled with quintessence. The four tests we apply are precession of the perihelion in the planetary orbits, gravitational redshift, deflection of light, and the Shapiro time delay. Through this process, we constrain the spacetime’s parameters in the context of the observational data, which results in about $$\sim 10^{-9}$$ ∼ 10 - 9 for the cloud of strings parameter, and $$\sim 10^{-20}$$ ∼ 10 - 20 m$$^{-1}$$ - 1 for that of quintessence. The response of the black hole to the gravitational perturbations is also discussed.

Perturbed thermodynamics and thermodynamic geometry of a static black hole in f (R) gravity

In this paper, we consider a static black hole in [Formula: see text] 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 behavior of this black hole. We observe that the singular point of the curvature scalar of Ruppeiner metric coincides completely with zero point of the heat capacity and the deviation occurs with increasing correction parameter.

Capture of Massless and Massive Particles by Parameterized Black Holes

We study an influence of the leading coefficient of the parameterized line element of the spherically symmetric, static black hole on the capture of massless and massive particles. We have shown that negative (positive) values of ϵ decreases (increases) the radius of characteristic circular orbits and consequently, increases (decreases) the energy and decreases (increases) the angular momentum of the particle moving along these orbits. Moreover, we have calculated and compared the capture cross section of the massive particle in the relativistic and non-relativistic limits. It has been shown that in the case of small deviation from general relativity the capture cross section for the relativistic and nonrelativistic particle has an additional term being linear in the small dimensionless deviation parameter ϵ.

The Hilbert manifold of asymptotically flat metric extensions

In [Commun Anal Geom 13(5):845–885, 2005], Bartnik described the phase space for the Einstein equations, modelled on weighted Sobolev spaces with local regularity $$(g,\pi )\in H^2\times H^1$$ ( g , π ) ∈ H 2 × H 1 . In particular, it was established that the space of solutions to the constraints form a Hilbert submanifold of this phase space. The motivation for this work was to study the quasi-local mass functional now bearing his name. However, the phase space considered there was over a manifold without boundary. Here we demonstrate that analogous results hold in the case where the manifold has an interior compact boundary, and the metric is prescribed on the boundary. Then, still following Bartnik’s work, we demonstrate the critical points of the mass functional over this space of extensions correspond to stationary solutions with vanishing Killing vector on the boundary. Furthermore, if this solution is smooth then it is in fact a static black hole solution. In particular, in the vacuum case, critical points only occur at exterior Schwarzschild solutions; that is, critical points of the mass over this space do not exist generically. Finally, we briefly discuss a version of the result when the boundary data is related to Bartnik’s geometric boundary data. In particular, by imposing different boundary conditions on the Killing vector, we show that stationary solutions in this case correspond to critical points of an energy resembling the difference between the ADM mass and the Brown–York mass of the boundary.