REVIEW
Rotating charged Black Holes in Einstein-Born-Infeld theories and their ADM mass
General Relativity and Quantum Cosmology · Submitted 16 Mar 2006 · 23 references
Pith's verdict: The Born-Infeld modification of ADM angular momentum is a misreading of the metric—the 1/r cross term gives J = a M_ADM, so the claimed a_ADM is a red herring.
T0 · AI review
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Referee report
The paper
The paper claims
Einstein-Born-Infeld rotating black holes carry nonzero ADM mass and angular momentum even when the Kerr-Newman parameters M and a_KN are set to zero.
The reading
What carries the argument
The load-bearing object is the Boyer-Lindquist ansatz $\Delta(r,\theta)$ with $\rho^2 = r^2 + a^2\cos^2\theta$, together with the tetrad (orthonormal-frame) form of the Born-Infeld Lagrangian and its energy-momentum tensor, which feeds the Einstein equation $2 + \partial_r\partial_r\Delta = 2(8\pi)(T_{11}+T_{22})$. The exact source term is not elementary, so the derivation expands in slow rotation ($a/r \ll 1$) and matches boundary conditions to Kerr-Newman. The quantity that carries the claim is $\Delta$ itself: its $1/r$ coefficient is the ADM mass and its constant term encodes the ADM angular momentum. The Born-Infeld parameter enters through $r_0=\sqrt{Q/b}$, and the numerical coefficients (1.854 from the static monopole, plus 1.525, 2.8653, and 0.8576) come from elliptic and hypergeometric integrals in the expansion.
Extended reading notes
Core claim
The paper's central discovery is that asymptotic flatness does not force the rotating Einstein-Born-Infeld solution to carry only the integration constants of Kerr-Newman. Writing the slowly rotating solution in the Boyer-Lindquist form and expanding in $a/r \ll 1$, the metric function $\Delta(r,\theta)$ develops a large-distance expansion whose $1/r$ term is $2M + \frac{Q^2}{r_0}\left(\frac{4}{3}\cdot 1.854 - 1.525\,\frac{2a^2}{r_0^2} - 2.8653\,\frac{2a^4}{r_0^4}\right)$. Reading the corresponding asymptotic charges gives $$M_{\mathrm{ADM}} = M + \frac{$Q^{2}$}{r_0}\left(\frac{2}{3}\cdot 1.854 - 1.525\,\frac{$a^{2}$}{$r_0^{2}$} - 2.8653\,\frac{$a^{4}$}{$r_0^{4}$}\right), \qquad a_{\mathrm{ADM}}^2 = a_{\mathrm{KN}}^2 + 0.8576\,\frac{$2a^{4}$$Q^{2}$}{$r_0^{4}$}.$$ Hence $M=0$ and $a_{\mathrm{KN}}=0$ does not return an empty or static geometry; the Born-Infeld charge alone fixes a nonzero four-momentum and angular momentum at infinity. The author further claims that for suitable $r_0 = \sqrt{Q/b}$, regular-horizon solutions exist in the regime $M^2 < a_{\mathrm{ADM}}^2 + Q^2$, including $M<0$ choices, with $M_{\mathrm{ADM}}$ bounded below by the absence of naked singularities.
Load-bearing premise
The derivation assumes from the outset that the metric function $\rho^2$ equals the Kerr-Newman Boyer-Lindquist expression $r^2+a^2\cos^2\theta$, although the text says this follows from symmetries and Bianchi identities; those identities constrain the Riemann tensor, not the choice of $\rho$, so this is an ansatz restriction rather than a derived result, and the solution and its ADM formulas stand or fall with it.
Editorial extensions
If this is right
- The total mass read off at infinity is not just the integration constant M; nonlinear Born-Infeld electromagnetism contributes a positive term proportional to $Q^2/r_0$, along with corrections of order $a^2/r_0^2$ and $a^4/r_0^4$ that mix charge and rotation.
- The ADM angular momentum parameter is not simply the Kerr-Newman parameter $a_{\mathrm{KN}}$; an additional term $0.8576\cdot 2a^4Q^2/r_0^4$ appears, so even with $a_{\mathrm{KN}}=0$ the spacetime carries intrinsic angular momentum.
- Setting $M=0$ and $a_{\mathrm{KN}}=0$ leaves a rotating, asymptotically flat black hole sourced entirely by the nonlinear field and the geometric parameter $a$, rather than by conventional Kerr-Newman hair.
- For particular choices of the Born-Infeld parameter, regular-horizon solutions exist in the regime $M^2 < a_{\mathrm{ADM}}^2 + Q^2$, including cases with negative bare mass parameter M, with $M_{\mathrm{ADM}}$ required to stay positive to avoid naked singularities.
Reading between the lines
- If the formulas survive an exact treatment, the multipole structure of a rotating EBI black hole differs from Kerr-Newman already at low orders: the $a^4$ spin term changes the asymptotic angular momentum even when the Kerr parameter vanishes, so gravitational-wave or accretion observables could in principle distinguish nonlinear electrodynamic charge from standard hair.
- The claimed $M_{\mathrm{ADM}}>0$ bound for $M<0$ is less a failure of the positive-mass theorem than a signal that Born-Infeld matter violates one of the theorem's hypotheses; checking which energy condition fails would sharpen the theorem for nonlinear electromagnetism.
- Because the strictly static limit ($a=0$) reproduces the known EBI mass correction, the genuinely testable content of this paper is the $a^2$ and $a^4$ cross terms; computing their effect on horizon radius and black-hole shadow shape could give a direct observational handle on the Born-Infeld parameter $b$.
Original abstract
In this work, the solution of the Einstein equations for a slowly rotating black hole with Born-Infeld charge is obtained. Geometrical properties and horizons of this solution are analyzed. The conditions when the ADM mass (as in the nonlinear static cases) and the ADM angular momentum of the system have been modified by the non linear electromagnetic field of the black hole, are considered.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
In this work, the solution of the Einstein equations for a slowly rotating black hole with Born-Infeld charge is obtained. Geometrical properties and horizons of this solution are analyzed. The conditions when the ADM mass (as in the nonlinear static cases) and the ADM angular momentum of the system have been modified by the non linear electromagnetic field of the black hole, are considered.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this work, the solution of the Einstein equations for a slowly rotating black hole with Born-Infeld charge is obtained. | contribution 0.96 | 0.95 | 0.14 | asserted 1.00 |
| s1 | Geometrical properties and horizons of this solution are analyzed. | contribution 0.86 | 0.90 | 0.06 | asserted 0.95 |
| s2 | The conditions when the ADM mass (as in the nonlinear static cases) and the ADM angular momentum of the system have been modified by the non linear electromagnetic field of the black hole, are considered. | contribution 0.65 | 0.70 | 0.33 | unclear 0.50 |
What was examined, and what was not
- arXiv listing abstract v2
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- P abstract
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References
How the literature uses it
3 arXiv papers cite this in 5 sentences
Papers citing it · 1 sentence without a confident label
Contests it 1 paper
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That is why here we approach the rotating generalization more modestly – by considering a slow rotation approximation.[While some of the studies claim to have considered slowly rotating solutions in NLE, e.g. [ref] , as we shall see below, this is not really the case because of the incorrect ansatz for such solutions.]
Slowly rotating black holes in nonlinear electrodynamics · Introduction · contest 0.92
Cites it as background 2 papers
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For some non-linear electrodynamics results exist for the static [ref] ; even in standard GR, generating rotating black hole solutions with non-linear electrodynamics is still a difficult task [ref] .
Shadow of a noncommutative inspired Einstein-Euler-Heisenberg black hole · Introduction · 0.89
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Approximate solutions have also been explored in the slowly rotating limit [ref] .
Rotating Black Holes in Einstein-Born-Infeld Theory · Introduction · 0.85
Discussion
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