A point mass and continuous collapse to a point mass in general relativity

Abstract

An original way of presentation of the Schwarzschild black hole in the form of a point-like mass with making the use of the Dirac $\delta$-function, including a description of a continuous collapse to such a point mass, is given. A maximally generalized description restricted by physically reasonable requirements is developed. A so-called field-theoretical formulation of general relativity, being equivalent to the standard geometrical presentation of general relativity, is used. All of the dynamical fields, including the gravitational field, are considered as propagating in a background (curved or flat) spacetime. Namely these properties allow us to present a non-contradictive picture of the point mass description. The results can be useful for studying the structure of the black hole true singularities and could be developed for practical calculations in models with black holes.

arXiv comment25 pages. arXiv admin note: text overlap with arXiv:gr-qc/0410041 by other authors

References in corpus (21)

• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Tests of general relativity with GW150914
• Self-Interaction and Gauge Invariance
• Dimensional regularization of the gravitational interaction of point masses
• The river model of black holes
• On the Distributional Nature of the Energy Momentum Tensor of a Black Hole or What Curves the Schwarzschild Geometry ?
• Remarks on the distributional Schwarzschild geometry
• Gravitational collapse in Painlevé-Gullstrand coordinates
• Null Cones and Einstein's Equations in Minkowski Spacetime
• Weakly decaying asymptotically flat static and stationary solutions to the Einstein equations
• Self-Renormalization of the Classical Quasilocal Energy
• Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories
• Generalized Painlevé-Gullstrand metrics
• A Time-Like Naked Singularity
• Point massive particle in General Relativity
• Distributional Sources in General Relativity: two point-like examples revisited
• The Gravitational Field of Massive Non-Charged Point Source in General Relativity
• The Schwarzschild black hole as a point particle
• Two-dimensional description of D-dimensional static black holes with pointlike sources
• Rigid covariance as a natural extension of Painlevé--Gullstrand space-times: gravitational waves

Cited by in corpus (2)

• The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review
• Black holes of the Vaidya type with flat and (A)dS asymptotics as point particles