Falling into a Schwarzschild black hole

Müller, Thomas

doi:10.1007/s10714-008-0623-7

Cited by 28 publications

(29 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In axially symmetric, rotating case, the vacuum spacetime is determined by the Kerr-de Sitter (KdS) geometry [34]. In the spacetimes with the repulsive cosmological term (and the related solutions of the f(R) gravity), motion of photons is treated in a series of papers [35][36][37][38][39][40][41][42][43][44][45], while motion of test particles was studied in [15,31,. Oscillatory motion of current carrying string loops in SdS and KdS spacetimes was treated in [69][70][71][72][73][74][75].…”

Section: Introductionmentioning

confidence: 99%

General relativistic polytropes with a repulsive cosmological constant

2016

View full text Add to dashboard Cite

Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters-the polytropic index n, the ratio of central pressure and central energy density of matter σ, and the ratio of energy density of vacuum and central density of matter λ. The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with n = 0 corresponding to the configurations with uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of n > 0, the static equilibrium configurations with fixed parameters n, σ, are allowed only up to a critical value of the cosmological parameter λc = λc(n, σ). In the case of n > 3, the critical value λc tends to zero for special values of σ. The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with extension comparable to those of the dark matter halos related to galaxies, i.e., with extension ℓ > 100 kpc and mass M > 10 12 M⊙. For such largely extended polytropes the cosmological parameter relating the vacuum energy to the central density has to be larger than λ = ρvac/ρc ∼ 10 −9 . We demonstrate that extension of the static general relativistic polytropic configurations cannot exceed the so called static radius related to their external spacetime, supporting the idea that the static radius represents a natural limit on extension of gravitationally bound configurations in an expanding universe dominated by the vacuum energy.PACS numbers: 98.80. Es,

show abstract

Section: Introductionmentioning

confidence: 99%

General relativistic polytropes with a repulsive cosmological constant

2016

View full text Add to dashboard Cite

show abstract

“…Eqs. (25), (26) and Fig. 4 show that the real part of the quasinormal resonant frequency, Re(ω), is an (almost linearly) monotonically increasing function of the dimensionless mass parameter of the scalar field µ.…”

Section: The Quasinormal Resonances Of Massive Scalar Fields In Tmentioning

confidence: 89%

“…The cosmological consequences of the relict cosmological constant have been studied both for the cosmological models [4], and the Einstein-Straus vacuola models [5][6][7][8][9][10][11], or the more general McVittie model [12] of mass concentrations immersed in the expanding universe [13][14][15][16][17][18][19]. It has been shown that the repulsive cosmological constant can have an important role also in astrophysical processes (optical effects, accretion, jets) related to supermassive black holes in active galactic nuclei [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. The role of the relict cosmological constant in motion of interacting galaxies has been studied in [39,40], using an appropriately defined Pseudo-Newtonian potential [41].…”

Section: Introductionmentioning

confidence: 99%

Slowly decaying resonances of massive scalar fields around Schwarzschild-de Sitter black holes

Toshmatov¹,

Stuchlík²

2017

Eur. Phys. J. Plus

View full text Add to dashboard Cite

We study in special limiting cases quasinormal modes of massive scalar fields in the Schwarzschild-de Sitter black hole backgrounds. We determine the lower limit on the mass parameter of the scalar field that allows the waves with quasinormal frequencies to propagate to infinity, showing that it depends on the spacetime parameters only. Then we discuss in the large multipole number limit quasinormal modes whose frequencies can be directly related to the unstable circular photon geodesics. In the large scalar mass approximation, we demonstrate new interesting phenomenon of slowly decaying resonances, that are strongly related to the maximum of the effective potential of the massive scalar field, which is located at the static radius of the Schwarzschild-de Sitter spacetimes, where the cosmic repulsion is just balanced by the black hole attraction.

show abstract

“…This is likely to be true, however, we argue that understanding any exact solution of general relativity deserves to be studied and their unlikeliness should not preclude us from doing so. Moreover, visualizing space-time is one of the best tools to understand some of their properties [17][18][19], and the more complicated the metric is, the more useful will the visualization tools be. This paper is therefore aimed at filling this gap, as well as exploring the variety of phenomena that arise when one considers the full set of parameters of the metric as well as its maximal analytic extension.…”

Section: Introductionmentioning

confidence: 99%

Seeing relativity-II: Revisiting and visualizing the Reissner–Nordström metric

Riazuelo

2019

Int. J. Mod. Phys. D

View full text Add to dashboard Cite

In this paper we study some features of the Reissner-Nordström metric both from an analytic and a visual point of view. We perform an accurate ray tracing and study of null geodesics in various situations. Among the issues we focus on are (i) the comparison with the Schwarzschild case, (ii) the naked singularity case, where, if the electric charge is not too large, some dark shell appears on images despite there is no horizon in the metric, and (iii) the wormhole crossing case, i.e., a visual exploration of the maximal analytic extension of the metric.For any non zero value of M or Q, the region r = 0 is a curvature singularity. Consequently, one has a black hole when horizon(s) surround the singularity, i.e., when M ≥ |Q|. In the opposite case (M < |Q|), one has a naked singularity, whose visual aspect shall be studied in the next sections together with the black hole case. B. Classifying null geodesicsBeing spherically symmetric, any test particle of four-velocity or four-momentum experiences a planar geodesic motion in the metric, so that we can reduce our analysis to the case where the particle is confined within the plane θ = π/2. Also, the metric being static, one can extract two constants of motion for a massive test particle of four-velocity u µ or massless particle of four-wavevector k µ . Those are • The particle total energy per unit of mass or its total energy E := g µt u µ , or E := g µt k µ• The particle projected angular momentum per unit of mass, or its projected total angular momentum, L := −g µϕ u µ , or L := −g µϕ k µ .

show abstract

Falling into a Schwarzschild black hole

Cited by 28 publications

References 16 publications

General relativistic polytropes with a repulsive cosmological constant

General relativistic polytropes with a repulsive cosmological constant

Slowly decaying resonances of massive scalar fields around Schwarzschild-de Sitter black holes

Seeing relativity-II: Revisiting and visualizing the Reissner–Nordström metric

Contact Info

Product

Resources

About