Author

# Valeri P. Frolov

Other affiliations: University of Minnesota, François Rabelais University, Kavli Institute for Theoretical Physics ...read more

Bio: Valeri P. Frolov is an academic researcher from University of Alberta. The author has contributed to research in topics: Black hole & Extremal black hole. The author has an hindex of 53, co-authored 231 publications receiving 9509 citations. Previous affiliations of Valeri P. Frolov include University of Minnesota & François Rabelais University.

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##### Papers

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TL;DR: A brief history of black hole physics can be found in this paper, where the authors discuss the properties of black holes and their properties in terms of physics, physics theory, and physics of the interior of a black hole.

Abstract: Preface. I. Basic Concepts. 1. Introduction: Brief History of Black Hole Physics. 2. Spherically Symmetric Black Holes. 3. Rotating Black Holes. 4. Black Hole Perturbations (with N. Andersson). 5. General Properties of Black Holes. 6. Stationary Black Holes. 7. Physical Effects in the Gravitational Field of a Black Hole. 8. Black Hole Electrodynamics. 9. Astrophysics of Black Holes. II. Further Developments. 10. Quantum Particle Creation by Black Holes. 11. Quantum Physics of Black Holes. 12. Thermodynamics of Black Holes. 13. Black Holes in Unified Theories. 14. The Interior of a Black Hole. 15. Ultimate Fate of Black and White Holes. 16. Black Holes, Wormholes, and Time Machines. Conclusions. Appendices: A: Mathematical Formulas. B: Spherically Symmetric Spacetimes. C: Rindler Frame in Minkowski Spacetime. D: Kerr-Newman Geometry. E: Newman-Penrose Formalism. F: Wave Fields in a Curved Spacetime. G: Wave Fields in the Kerr Metric. H: Quantum Fields in Kerr Spacetime. I: Quantum Oscillator. Bibliography. Index.

460 citations

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TL;DR: It is shown that instead of the singularity the closed world can be formed inside the black hole and it is argued that this property of this model may also be valid in a more general case provided the gravitation theory is asymptotically free and the limiting curvature exists.

Abstract: The internal structure of spacetime inside a black hole is investigated on the assumption that some limiting curvature exists. It is shown that the Schwarzschild metric inside the black hole can be attached to the de Sitter one at some spacelike junction surface which may represent a short transition layer. The method of massive thin shells by Israel is used to obtain the characteristics of this layer. It is shown that instead of the singularity the closed world can be formed inside the black hole. It is argued that this property of our model may also be valid in a more general case provided the gravitation theory is asymptotically free and the limiting curvature exists. After passing the deflation stage the closed world in the black-hole interior may begin to inflate and give rise to a new macroscopic universe. The described model may be considered as an example of the creation of a closed or semiclosed world "in the laboratory." The possible fate of the evaporating black hole is also briefly discussed.

330 citations

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TL;DR: In this article, it is shown that the Schwarzchild metric inside a black hole can be attached to the de Sitter one at some spacelike junction surface which may represent a short transition layer.

239 citations

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TL;DR: In this paper, the authors consider static spherically symmetric metrics which represent nonsingular black holes in four-and higher-dimensional spacetime and show that such a metric cannot describe a non-singular black hole.

Abstract: We discuss static spherically symmetric metrics which represent nonsingular black holes in four- and higher-dimensional spacetime. We impose a set of restrictions, such as a regularity of the metric at the center $r=0$ and Schwarzschild asymptotic behavior at large $r$. We assume that the metric besides mass $M$ contains an additional parameter $\ensuremath{\ell}$, which determines the scale where modification of the solution of the Einstein equations becomes significant. We require that the modified metric obeys the limiting curvature condition; that is, its curvature is uniformly restricted by the value $\ensuremath{\sim}{\ensuremath{\ell}}^{\ensuremath{-}2}$. We also make a ``more technical'' assumption that the metric coefficients are rational functions of $r$. In particular, the invariant $(\ensuremath{
abla}r{)}^{2}$ has the form ${P}_{n}(r)/{\stackrel{\texttildelow{}}{P}}_{n}(r)$, where ${P}_{n}$ and ${\stackrel{\texttildelow{}}{P}}_{n}$ are polynomials of the order of $n$. We discuss first the case of four dimensions. We show that when $n\ensuremath{\le}2$ such a metric cannot describe a nonsingular black hole. For $n=3$ we find a suitable metric, which besides $M$ and $\ensuremath{\ell}$ contains a dimensionless numerical parameter. When this parameter vanishes, the obtained metric coincides with Hayward's one. The characteristic property of such spacetimes is $\ensuremath{-}{\ensuremath{\xi}}^{2}=(\ensuremath{
abla}r{)}^{2}$, where ${\ensuremath{\xi}}^{2}$ is a timelike at infinity Killing vector. We describe a possible generalization of a nonsingular black-hole metric to the case when this equality is violated. We also obtain a metric for a charged nonsingular black hole obeying similar restrictions as the neutral one and construct higher dimensional models of neutral and charged black holes.

232 citations

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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

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28,685 citations

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TL;DR: The first direct detection of gravitational waves and the first observation of a binary black hole merger were reported in this paper, with a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ.

Abstract: On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160) Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

4,375 citations

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TL;DR: Van Kampen as mentioned in this paper provides an extensive graduate-level introduction which is clear, cautious, interesting and readable, and could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes.

Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

3,647 citations

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TL;DR: A review of cosmological constants can be found in this paper, where the authors discuss several aspects of the Cosmological Constant problem from both cosmology and theoretical perspectives.

3,130 citations