
550 S.E.2d 425 (2001)
250 Ga. App. 53
ALLSUP
v.
The STATE.
No. A01A1021.
Court of Appeals of Georgia.
June 8, 2001.
*426 Tolbert & Elrod, Scott R. Tolbert, Christopher D. Elrod, Jefferson, for appellant.
Timothy G. Madison, Dist. Atty., Robin R. Riggs, Asst. Dist. Atty., for appellee.
JOHNSON, Presiding Judge.
A jury convicted David Allsup of three counts of aggravated assault, two counts of kidnapping, and four counts of cruelty to children. He appeals, alleging the trial court erred in denying his motion for new trial based on the general grounds and based on the ineffectiveness of his trial counsel, and erred in not appointing him new counsel for trial. Because each of these enumerations of error lacks merit, we affirm Allsup's convictions.
Viewed in a light most favorable to support the jury's verdict, the evidence shows that Allsup's girlfriend and her three children met Allsup as they were walking home from a store. Allsup began screaming and cursing at his girlfriend. He grabbed her by the hair and pulled her behind a church building so they could not be seen from the road. The children, unsure about what to do, followed their mother.
Allsup began kicking, slapping, punching and hitting his girlfriend. He also hit her numerous times with the metal end of a lighter. She tried to get away, but when she fell down, Allsup kicked her in the ribs and pulled her back up by her hair. Her head was bleeding, and her two older children were crying and screaming.
When Allsup finished striking his girlfriend, he began hitting her 12-year-old son. He pulled the boy by the hair and kicked, punched and hit him in the chest, stomach, *427 back and head. Allsup hit the boy in the head numerous times. He also hit him with the metal end of a lighter. When the boy fell down, Allsup kicked him in the side and jerked him back up by his hair. The boy's head and mouth were bleeding.
Allsup then grabbed his girlfriend's ten-year-old daughter by the hair and dragged her behind the church. He slapped her across the face and hit her with the metal end of a cigarette lighter. His leg was over her arms so she could not move. Despite her cries to stop, Allsup hit her in the face and head, causing her lip to bleed.
When Allsup finished hitting the daughter, he resumed assaulting his girlfriend, then her son, then her daughter again. He pulled the boy by the hair a good distance the second time before he began striking him. Allsup said that if the 16-month-old baby had been older, she would have gotten the same thing.
When Allsup was finally finished, they all walked back toward the trailer where they were living. Upon seeing police, Allsup fled. He was apprehended approximately four weeks later in Tennessee. Allsup's girlfriend and her children were taken to a safe house and then transported to a hospital. All three suffered physical injuries, including swelling, bruises and cuts.
1. Allsup claims that no evidence supports the verdicts of aggravated assault against the victims. OCGA § 16-5-21(a)(2) provides, in part, that
"[a] person commits the offense of aggravated assault when he or she assaults ... [w]ith a deadly weapon or with any object, device, or instrument which, when used offensively against a person, is likely to or actually does result in serious bodily injury."
Allsup claims that a cigarette lighter is not likely to cause serious bodily injury if used offensively and that none of the victims sustained serious bodily injuries. According to him, the jury should have convicted him of the lesser included offense of battery. We disagree.
The victims testified that the girlfriend was hit more than 20 times with the cigarette lighter, that her head was bleeding as a result and that her hair was filled with blood. Because the girlfriend tried to cover her head with her hands, her hands had extensive swelling and bruising, and one of her fingers was broken. The victims further testified that Allsup hit the 12-year-old boy in the head with the cigarette lighter more than 20 times and that the boy's head and mouth were bleeding. The victims also testified that Allsup hit the ten-year-old girl with the cigarette lighter. Officers and investigators testified that (1) all three victims suffered visible bruising to their faces, (2) the twelve-year-old boy had a cut on the top of his head, (3) there was concern about possible hearing loss in the twelve-year-old boy, and (4) the ten-year-old girl had black eyes and bloody lips. Photographs also corroborated the extent of the victims' injuries. One officer testified that his report listed the victims' injuries only as superficial because the other boxes he could have checked involved death, knife wounds and broken bones.
This evidence was sufficient to support Allsup's convictions for aggravated assault.[1] It was within the jury's province to find that the cigarette lighter constituted an offensive weapon likely to cause serious bodily injury[2] and that the victims received serious bodily injuries.[3] Moreover, Allsup's argument ignores the fact that evidence of an actual serious bodily injury is not required to sustain a conviction under OCGA § 16-5-21(a)(2).[4] As for Allsup's argument that OCGA § 16-5-21 is unconstitutionally vague, Allsup has waived this argument because he failed to raise it in the trial court.[5]
*428 2. Allsup claims that he was denied effective assistance of counsel because his trial attorney (1) failed to obtain evidence showing his girlfriend had previously made false accusations, and (2) failed to obtain a mental evaluation and medical records of Allsup. To establish ineffectiveness, Allsup must show that his trial counsel's performance was deficient and that the deficiency caused sufficient prejudice to deprive him of a fair trial.[6] The evidence must overcome the strong presumption that counsel's performance fell within the wide range of reasonable professional assistance.[7] We need not reach the deficiency issue absent a showing of prejudice.[8]
Here, we note at the outset that Allsup has failed to provide a transcript of the hearing on his motion for new trial, so we are unable to address the alleged deficiencies because these matters do not appear in the trial transcript.[9] The only evidence in the record before us shows that the public defender did not investigate alleged false allegations made by Allsup's girlfriend because the evidence would not have been admissible at Allsup's trial. The record also shows that Allsup failed to provide the public defender with "any ideas for any sort of a defense." In the absence of a transcript on Allsup's motion for new trial hearing, we must assume that he failed to meet his burden of proving these alleged ineffective acts and that the trial court correctly denied the motion for new trial on the basis of ineffective assistance of counsel.[10]
Moreover, we find that the overwhelming evidence prevents Allsup from establishing a reasonable likelihood that the trial's outcome would have been different had counsel obtained evidence of the victim's alleged prior false allegations or medical records and a mental evaluation of Allsup.[11]
3. Allsup contends the trial court erred in failing to appoint new counsel for trial. The record shows that a public defender was appointed to represent Allsup. One week prior to trial, a hearing was held to give Allsup an opportunity to voice his concerns about his appointed counsel. Specifically, Allsup argued that he wanted another attorney but he did not have any money. The trial court informed Allsup that the public defender was the only one in the circuit and that she was exceptional. The court then gave Allsup three choices: (1) to allow the public defender to represent him, (2) to hire his own attorney, or (3) to represent himself. Allsup decided to continue with the representation of the public defender. Allsup requested new counsel again during trial, but the trial court responded that Allsup could either represent himself or hire an attorney; the trial court instructed Allsup that the state would not provide another attorney for him. It is well-established that
a criminal defendant does have a constitutional right to be defended by counsel of his own selection whenever he is willing and able to employ such counsel. However, an indigent criminal defendant does not have an absolute right to discharge one court-appointed counsel and have another substituted in his place. A request of this sort addresses itself to the sound discretion of the trial court.[12]
Upon review of the record and transcripts in this case, we find that the trial court did not abuse its discretion in denying Allsup's request for a different public defender.
Judgment affirmed.
RUFFIN and ELLINGTON, JJ., concur.
NOTES
[1]  See Price v. State, 237 Ga.App. 54, 55(1), 513 S.E.2d 40 (1999).
[2]  See Johnson v. State, 246 Ga.App. 109, 111(2), 539 S.E.2d 605 (2000); Wheeler v. State, 232 Ga.App. 749, 503 S.E.2d 628 (1998).
[3]  See Price, supra.
[4]  Reynolds v. State, 234 Ga.App. 884, 885(1)(b), 508 S.E.2d 674 (1998).
[5]  Boxer X v. State, 237 Ga.App. 526, 529-530(5), 515 S.E.2d 668 (1999).
[6]  Price, supra at 56(5), 513 S.E.2d 40.
[7]  Id.
[8]  Trammel v. State, 265 Ga. 156(1), 454 S.E.2d 501 (1995).
[9]  See Sanders v. State, 245 Ga.App. 701, 703(4), 538 S.E.2d 772 (2000).
[10]  Roberts v. State, 244 Ga.App. 330, 332(2)(c), 534 S.E.2d 526 (2000).
[11]  See Price, supra.
[12]  (Citations omitted.) Mitchell v. State, 242 Ga. App. 177, 183(6), 529 S.E.2d 169 (2000); Parham v. State, 218 Ga.App. 42, 44(4), 460 S.E.2d 78 (1995).
