Black holes, first-order flow equations and geodesics on symmetric spaces

Following the same treatment of Bellucci et al. we obtain, the hitherto unknown general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing and vanishing central charge Z for the so-called st2 model, the minimal rank-two [Formula: see text] symmetric supergravity in d = 4 space-time dimensions. We also make useful comparisons with results that already exist in literature, and introduce the fake supergravity (first-order) formalism to be used in our analysis. An analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane charge configurations has also been presented.

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First order flow for non-extremal AdS black holes and mass from holographic renormalization

Journal of High Energy Physics ◽

10.1007/jhep10(2014)075 ◽

2014 ◽

Vol 2014 (10) ◽

Cited By ~ 13

Author(s):

Alessandra Gnecchi ◽

Chiara Toldo

Keyword(s):

Black Holes ◽

Order Flow ◽

First Order ◽

Ads Black Holes ◽

Holographic Renormalization

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Second-order perturbations of Kerr black holes: Formalism and reconstruction of the first-order metric

Physical Review D ◽

10.1103/physrevd.103.104017 ◽

2021 ◽

Vol 103 (10) ◽

Author(s):

Nicholas Loutrel ◽

Justin L. Ripley ◽

Elena Giorgi ◽

Frans Pretorius

Keyword(s):

Black Holes ◽

Second Order ◽

First Order ◽

Kerr Black Holes

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BACH FLOWS OF PRODUCT MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887812500399 ◽

2012 ◽

Vol 09 (05) ◽

pp. 1250039 ◽

Cited By ~ 2

Author(s):

SANJIT DAS ◽

SAYAN KAR

Keyword(s):

Dynamical System ◽

Fixed Point ◽

Ricci Flow ◽

Flow Characteristics ◽

Geometric Flow ◽

Flow Equations ◽

First Order ◽

Bach Tensor ◽

Point Condition ◽

Future Work

We investigate various aspects of a geometric flow defined using the Bach tensor. First, using a well-known split of the Bach tensor components for (2, 2) unwarped product manifolds, we solve the Bach flow equations for typical examples of product manifolds like S2 × S2, R2 × S2. In addition, we obtain the fixed-point condition for general (2, 2) manifolds and solve it for a restricted case. Next, we consider warped manifolds. For Bach flows on a special class of asymmetrically warped 4-manifolds, we reduce the flow equations to a first-order dynamical system, which is solved exactly to find the flow characteristics. We compare our results for Bach flow with those for Ricci flow and discuss the differences qualitatively. Finally, we conclude by mentioning possible directions for future work.

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