The paper explores the evolution of rotating helium stars with masses greater than 10 solar masses, where the iron core collapse fails to produce a successful outgoing shock and instead forms a black hole of 2-3 solar masses. The study uses a two-dimensional hydrodynamics code (PROMETHEUS) to simulate the continued evolution of these stars, focusing on the formation of an accretion disk and the subsequent processes leading to gamma-ray bursts (GRBs). The key findings include: 1. **Angular Momentum and Disk Formation**: The outcome is sensitive to the angular momentum of the star. For low angular momentum ($j_{16} \leq 3$), material falls into the black hole without significant outflows. For high angular momentum ($j_{16} \geq 20$), centrifugal force halts the infalling matter outside 1000 km, leading to a low equatorial accretion rate and potential weak equatorial explosions. For intermediate angular momentum ($3 \leq j_{16} \leq 20$), a compact disk forms at a radius where neutrino losses are negligible, making these stars the best candidates for producing GRBs. 2. **Accretion and Energy Deposition**: The accretion rate into the black hole is crucial for GRB production. For the standard model with $\alpha = 0.1$ and $j_{16} = 10$, the average accretion rate is 0.07 solar masses per second, and the total energy deposited by neutrino annihilation is $(1-14) \times 10^{51}$ erg. The energy deposition is highly variable due to hydrodynamical instabilities, leading to significant variability in the time structure of the burst. 3. **Relativistic Jets and Supernovae**: The formation of relativistic jets is influenced by the accretion rate, angular momentum, and disk viscosity. These jets can penetrate the star within 5-10 seconds, leading to a supernova-like explosion. The energy of these jets can be up to a few times $10^{51}$ erg, with masses of about 1 solar mass and rich in 56Ni. 4. **Observational Consequences**: The study predicts a wide range of outcomes, from bright GRBs like GRB 971214 to faint GRB-supernovae like SN 1998bw. The energy deposition and jet formation are sensitive to the viewing angle, and the variability in the time structure of the burst can be significant. 5. **Black Hole Evolution**: The evolution of the black hole's mass and Kerr parameter is also explored, showing that the black hole can be spun up to high values, potentially leading to significant rotational energy extraction through MHD processes. The paper provides a detailed exploration of the mechanisms and conditions necessary forThe paper explores the evolution of rotating helium stars with masses greater than 10 solar masses, where the iron core collapse fails to produce a successful outgoing shock and instead forms a black hole of 2-3 solar masses. The study uses a two-dimensional hydrodynamics code (PROMETHEUS) to simulate the continued evolution of these stars, focusing on the formation of an accretion disk and the subsequent processes leading to gamma-ray bursts (GRBs). The key findings include: 1. **Angular Momentum and Disk Formation**: The outcome is sensitive to the angular momentum of the star. For low angular momentum ($j_{16} \leq 3$), material falls into the black hole without significant outflows. For high angular momentum ($j_{16} \geq 20$), centrifugal force halts the infalling matter outside 1000 km, leading to a low equatorial accretion rate and potential weak equatorial explosions. For intermediate angular momentum ($3 \leq j_{16} \leq 20$), a compact disk forms at a radius where neutrino losses are negligible, making these stars the best candidates for producing GRBs. 2. **Accretion and Energy Deposition**: The accretion rate into the black hole is crucial for GRB production. For the standard model with $\alpha = 0.1$ and $j_{16} = 10$, the average accretion rate is 0.07 solar masses per second, and the total energy deposited by neutrino annihilation is $(1-14) \times 10^{51}$ erg. The energy deposition is highly variable due to hydrodynamical instabilities, leading to significant variability in the time structure of the burst. 3. **Relativistic Jets and Supernovae**: The formation of relativistic jets is influenced by the accretion rate, angular momentum, and disk viscosity. These jets can penetrate the star within 5-10 seconds, leading to a supernova-like explosion. The energy of these jets can be up to a few times $10^{51}$ erg, with masses of about 1 solar mass and rich in 56Ni. 4. **Observational Consequences**: The study predicts a wide range of outcomes, from bright GRBs like GRB 971214 to faint GRB-supernovae like SN 1998bw. The energy deposition and jet formation are sensitive to the viewing angle, and the variability in the time structure of the burst can be significant. 5. **Black Hole Evolution**: The evolution of the black hole's mass and Kerr parameter is also explored, showing that the black hole can be spun up to high values, potentially leading to significant rotational energy extraction through MHD processes. The paper provides a detailed exploration of the mechanisms and conditions necessary for