Despite their consequential applications, metastable states of antibranes in warped throats are not yet fully understood. In this thesis, we provide new information on various aspects of these metastable antibranes through applications of the blackfold effective theory for higher-dimensional black holes. As concrete examples, we study the conjectured metastable state of polarised anti-D3 branes at the tip of the Klebanov-Strassler (KS) throat in type IIB supergravity and the analogous state of polarised anti-M2 branes at the tip of the Cvetic-Gibbons-Lu-Pope (CGLP) throat in eleven-dimensional supergravity. For anti-D3 branes in KS throat, we provide novel evidence for the existence of the metastable state exactly where no-go theorems are lifted. In the extremal limit, we recover directly in supergravity the metastable states originally discovered by Kachru, Pearson, and Verlinde (KPV). Away from extremality, we uncover a metastable wrapped black NS5 state. We observe that such metastability is lost when the wrapped NS5 is heated sufficiently that its horizon geometry resembles that of a black anti-D3. We study the classical stability of the KPV state under generic long-wavelength deformations. We observe that, with regards to considered perturbations and regime of parameters, the state is classically stable. A study of anti-M2 branes in CGLP throat reveals many similarities to that of the anti-D3 branes. We recover directly in supergravity the Klebanov-Pufu (KP) state at extremality, and our finite temperature results fit suggestively well with known, complementary no-go theorems. However, we discover an unexpected, exotic pattern of thermal transitions of the KP state different from that of the KPV. This thesis contains also a pedagogical introduction to the blackfold formalism, focusing on aspects immediately relevant to applications to metastable antibranes.
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